497 
L95c. 


ENGINEERING 
LIBRARY 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 

University  of  Gal. 

Berkeley 


The 

Compound  Engine 


By  F.  R.  Low 

Editor  of  POWER 


New  York 
Hill   Publishing  Company 


1906 


COPYRIGHT,  1900,  BY 
THB  POWER  PUBLISHING  COMPANY 


Engineering 
Library 

TJ 


THE  COMPOUND  ENGINE. 


BY    F.    R.     LOW. 


Before  we  commence  the  study  of  the  compound  engine  let  us 
brush  up  a  little  regarding  expansion  and  the  gains  and  losses 
attending  it. 

As  the  volume  of  steam  is  expanded  its  pressure  falls  and 
practically  in  an  inverse  ratio  ;  that  is,  if  you  double  the  volume 
you  halve  the  pressure,  if  you  treble  the  volume  you  have  one- 
third  the  pressure,  etc. ;  only  remember  that  you  must  work  with 
absolute  pressures,  not  gage  pressures. 

If  you  will  consider  that  statement  a  little  you  will  find  that  it 
means  that  the  product  of  the  volume  and  the  pressure  is  constant. 
Suppose  you  have  a  cubic  foot  of  steam  at  120  pounds  (absolute). 
Expand  it  to  two  cubic  feet  and  the  pressure  will  be  60,  but  you 
have  twojof  the  original  volumes  and  2x60  is  120.  If  you  expand 
it  to  three  cubic  feet  the  pressure  will  fall  to  40  pounds,  but  the 
product  of  this  pressure  and  the  three  volumes  is  still  120,  and 
however  far  we  may  expand  it  will  be  true  that,  counting  the 
original  volume  as  i,  the  pressure  times  the  number  of  volumes  to 
which -we  have  expanded  will  equal  the  initial  pressure.  The 
.number  of  times  that  the  original  volume  is  contained  in  the  final 
volume  is  called  the  "  ratio  of  expansion."  If  we  take  one  cubic 
foot  of  steam  and  expand  it  to  four  cubic  feet  the  ratio  of  expansion 
is  four,  etc.  From  this  principle  you  will  easily  see  that  we  can 
derive  the  following  • 

RULES. 

To  find  the  ratio  of  expansion  divide  the  final  volume  by  the 
initial  volume. 

What  is  the  ratio  of  expansion  when  two  cubic  feet  oi  stearr. 
are  expanded  to  eleven  cubic  feet  ? 

11-4-2  =  5,5 

713868 


RULES  FOR   RATIO  OF   EXPANSION,   TERMINAL   PRESSURE,    ETC. 


To  find  the  terminal  pressure  divide  the  initial  pressure  by 
the  ratio  of  expansion. 

EXAMPLE — Steam  of  75  pounds  gage  pressure  is  expanded  to 
six  times  its  original  volume.  What  will  its  pressure  be  ? 

A  gage  pressure  of  75  pounds  is  75+15=90  absolute,  approxi- 
mately, and  90-4-6=15  pounds  absolute  or  zero  gage. 

To  find  the  initial  pressure  multiply  the  terminal  pressure 
by  the  ratio  oj  expansion. 

EXAMPLE — In  an  engine  cylinder  steam  is  expanded  to  4.5 
times  its  volume  at  cut-off,  the  pressure  at  the  end  of  the  stroke 
being  18  pounds  absolute  What  is  the  initial  pressure? 

4. 5x1 8=8  c  pounds  absolute,  or  81  —  15=66  pounds  gage. 

In  Fig.  c  let  o  x  represent  the  absolute  zero  of  pressure  and 
o  A  the  zero  of  volume-  Suppose  we  have  a  volume  of  steam 
proportional  to  A  B  or  o  j  at  1 20  pounds  absolute.  If  it  is 


Fiq.  c. 


FIG.  2. 


expanded  to  twice  its  original  volume  its  volume  will  be  repre- 
sented by  the  line  o  2  and  its  pressure  will  be  i2O-r-2=6o  pounds. 
Setting  off  60  pounds  on  the  2d  ordinate  we  have  the  point  a  as 
representing  its  pressure  at  this  volume.  If  it  is  expanded  to  three 
times  its  original  size  its  volume  will  be  bounded  by  the  ordinate  3 
and  on  this  ordinate  we  set  off  the  pressure  120-1-3=40  pounds, 
locating  the  point  6.  Locating  in  the  same  manner  the  points 
c  defg,  representing  the  pressures  at  successive  volumes,  we  find 
that  if  joined  together  they  form  a  curve  which  constantly  ap- 
proaches, but  never  reaches  the  zero  line.  We  can  locate  as 
many  points  on  this  curve  as  we  like.  For  instance,  when  the 
volume  has  expanded  to  \y2  the  pressure  will  be  120^-1.5=80 
pounds,  which  set  off  on  the  corresponding  ordinate  gives  us  the 
point  h  This  curve  is  called  an  hyperbola,  and  represents,  when 


GAIN   BY   EXPANSION. 


used  in  this  way,  the  gradual  decrease  of  pressure  when  steam -is 
cut  off  and  expanded  in  an  engine  cylinder. 

Power,  you  know,  is  force  exerted  through  space.  In  Fig.  2 
we  have  a  force  of  80  pounds  gage  (95  pounds  absolute)  exerted 
throughout  the  stroke  o  x.  The  force  is  proportional  to  the  height 
of  the  line  o  A ;  the  space  through  which  it  is  exerted  is  propor- 
tional to  the  length  of  the  line  o  x,  the  power  which  is  the  product 
of  the  focce  and  space  is  proportional  then  to  the  product  of  o  A 
and  o  x,  which  is  the  area  of  the  rectangle  o  A  B  x. 

Now  suppose  that  instead  of  carrying  the  steam  the  full 
length  of  the  stroke  we  cut  it  off  at  half  stroke.  Then  during  the 
remainder  of  the  stroke  the  pressure  will  fall  off  along  the  line 
B  C,  Fig.  3,  and  the  power  will  be  proportional  to  the  area  A  B 


FIG.  3. 

Cx  D  O.  We  have  used  only  half  the  quantity  of  steam,  but  with 
the  exception  of  the  corner  B  E  C  have  got  as  much  power  as 
before.  The  area  B  C  x  D  is  all  gain,  so  you  see  there  is  a  very 
great  economy  in  cutting  off  at  half  stroke  over  carrying  steam  full 
stroke. 

Now  suppose  that  instead  of  cutting  off  at  one-half  stroke  as  in 
Fig.  3  we  cut  off  at  one-quarter  as  in  Fig.  4.  Here  again  the 
power  is  proportional  to  A  B  C  x  D  O.  The  area  B  C  x  D  is 
gain  from  expansion.  We  (have  used  half  as  much  steam  as  in 
Fig.  3  and  lost  the  area  B  F.  G  C.  There  is  still  a  distinct  gain, 
but  rather  less  than  before.  In  Fig.  3  with  half  the  steam  we  got 
in  the  diagram  A  B  C  x  D  O  85  per  cent,  of  the  power  we  would 
have  got  if  we  carried  steam  the  full  stroke.  In  Fig.  4,  we  halve 
the  steam  again  and  still  get  about  70  per  cent,  of  what  we  got  with 


LIMIT  OF  GAIN   BY   EXPANSION. 

double  the  quantity  in  Fig.  3,  and  about  60  per  cent,  of  what  we.' 
got  with  four  times  as  much  steam  in  Fig.  2. 

When  the  steam  follows. full  stroke  all  its  expansive  power  is 
sacrificed  and  we  lose  the  area  which  would  be  included  between 
the  diagram  and  the  dotted  line  B  KFig.  i  if  that  dotted  line  were 
extended  until  it  met  the  back  pressure  line,  which  would  be  some- 
what higher  than  the  line  O  x  even  with  a  condensing  engine. 
When  expansion  is  introduced  this  loss  is  lessened.  If  Cy  in 
Fig.  3  were  extended  to  meet  a  back  pressure  line,  m  n  at  atmos- 
pheric pressure,  the  area  would  be  obviously  smaller,  and  in  Fig.  4 
the  area  is  shown  to  be  smaller  still.  In  all  the  diagrams  the 
volume  to  be  filled  with  steam  is  proportional  to  the  line  A  B, 


FIG.  4. 

and  the  power  is  proportional  to  the  area  of  the  diagram  and 
theoretically  the  line  A  B  will  be  shortest  per  unit  of  area  of 
diagram,  i.  e. ,  the  volume  of  steam  called  for  will  be  least  per  unit 
of  power  developed,  when  trie  expansion  line  just  meets  the  line  of 
back  pressure,  and  the  diagram  ends  in  a  point  as  in  Fig.  5  ;  in 
other  words  when  the  terminal  pressure  just  equals  the  back 
pressure.  The  number  of  expansions  necessary  to  do  this  can 
easily  be  found  by  dividing  the  absolute  initial  pressure  by  the 
absolute  back  pressure. 

There  are  several  reasons  why  this  theoretical  consideration 
does  not  hold  good  in  practice.  In  the  first  place,  if  you  had  your 
steam  given  to  you  it  would  still  cost  you  something  to  run  an 
engine.  There  is  the  interest  on  the  investment,  depreciation, 
repairs,  attendance,  oil,  waste,  etc.  The  sum  of  these  fixed  charges 
per  horse-power  for  a  given  engine  will  be  least  when  the  engine 


CYLINDER    CONDENSATION.  5 

is  delivering  the  greatest  number  of  horse-power,  or  in  other 
words,  when  it  has  the  greatest  mean  effective  pressure.  r  But  the 
earlier  the  cut-off,  the  less  the  mean  effective  pressure,  the  less  the 
horse-power,  and  the  greater  the  fixed  charges  per  horse-power. 
This  factor  is  not  of  extreme  importance,  however,  for  the  fixed 
charges  would  not  be  very  much  greater  for  a  larger  engine  out  of 
which  we  could  get  the  same  horse-power,  with  a  lower  mean 
effective,  and  the  earlier  cut-off.  The  principal  difficulty  comes 
from  cylinder  condensation,  which  was  considered  somewhat  at 
length  in  the  last  lecture.  The  incoming  steam  at  a  temperature 


FIG.  6. 

due  to  the  boiler  pressure  strikes  against  the  cylinder  walls  which 
have  just  been  exposed  to  the  exhaust  temperature,  and  condenses 
until  enough  heat  is  given  up  to  heat  the  surfaces  up  to  the 
temperature  of  the  incoming  steam.  The  steam  so  condensed  is 
re-evaporated  for  the  most  part  on  the  exhaust  stroke,  and  thus 
gets  through  the  cylinder  without  doing  any  work.  The  amouut 
of  this  condensation  depends  upon  the  change  in  the  temperature 
of  the  cylinder  walls.  If  the  cylinder  could  be  made  of  a  non- 
conducting material,  a  material  which  was  slow  to  absorb  and 
radiate  heat,  there  would  be  little  condensation.  You  know  that 
polished  surfaces  radiate  and  absorb  less  than  rough  ones,  and  on 
several  recent  high-grade  engines  the  inside  of  the  cylinder  heads, 
the  piston  heads  and  all  the  surfaces  exposed  to  live  steam  in  the 
cylinder  have  been  highly  finished,  with  beneficial  results.  The 
shorter  the  time  required  for  the  revolution,  the  less  the  condensa- 


6  EFFECT  OF  CYLINDER  CONDENSATION. 

tion.  While  it  is  true  that  whether  the  engine  runs  fast  or  slow 
the  walls  will  be  exposed  half  of  the  time  to  the  temperature  of  the 
steam  and  half  to  the  temperature  of  the  exhaust,  it  is  also  true 
that  the  temperature  of  the  walls  will  vary  least  when  the  revolution 
is  completed  in  the  shortest  time. 

As  the  steam  expands  its  temperature  decreases  and  the  sur- 
faces begin  to  cool,  continuing  to  do  so  throughout  the  expansion 
and  the  exhaust  stroke.  The  longer  it  takes  to  make  the  revolu- 
tion the  cooler  these  surfaces  will  get.  In  a  pumping  engine 
making  30  revolutions  a  minute  the  surfaces  are  exposed  to  the 
exhaust  temperature  for  a  full  second,  and  to  a  temperature  below 
the  initial  for  the  greater  part  of  another  second  during  the  work- 
ing stroke.  In  an  engine  running  300  revolutions  per  minute  the 
surfaces  have  only  one-tenth  the  time  in  which  to  heat  and  cool, 
the  variation  of  temperature  is  less  and  less  steam  is  condensed  in 
raising  their  temperature.  The  surfaces  never  get  up  to  the 
temperature  of  the  steam  nor  down  to  that  of  the  exhaust,  but  vary 
back  and  forth  through  an  intermediate  range,  the  magnitude  of 
which  depends  largely  on  the  time  of  exposure.  Experiments 
made  by  Messrs.  Gately  and  Kletsch  upon  an  unjacketed  simple 
engine  at  Sandy  Hook  showed  that  the  condensation  varied 
sensibly  inversely  as  the  rotative  speed.*  Obviously,  too,  the 
emission  of  heat  from  the  surfaces  and  the  condensation  necessary 
to  restore  their  temperature  will  be  greater  with  greater  differences 
between  the  initial  and  exhaust  temperatures ;  the  higher  the 
steam  pressure  and  the  lower  the  back  pressure  the  greater  the 
condensation. 

The  ratio  of  expansion  has  an  important  bearing  on  the  per- 
centage of  loss  by  cylinder  condensation.  Not  only  is  the  actual 
amount  of  steam  lost  in  this  way  increased  with  shorter  cut-offs  by 
the  fact  that  the  temperature  is  below  that  of  the  initial  for  a 
greater  portion"  of  the  stroke,  but  as  less  steam  is  used  per  stroke 
with  an  early  cut-off,  the  steam  condensed  in  warming  up  the 
surfaces  is  a  greater  proportion  of  the  total  amount.  Suppose  you 
have  an  engine  where  the  stroke  is  twice  the  diameter,  which  is  a 
common  proportion.  When  it  is  cutting  off  at  one-quarter  stroke 
the  area  of  the  cylinder  wall  exposed  up  to  cut-off  will  just  equal 

*  A  Manual  of  the  Steam  Engine.     R.  H.  Thurston.     Part  i,  page  507. 
Journal  Franklin  Institute,  October,  1885. 
Cylinder  Condensation. 


SURFACE  INVOLVED  IN   INITIAL  CONDENSATION.  JT 

the  area  of  the  piston  head  and  the  cylinder  head.*  In  addition, 
there  are  the  counterbore,  ports,  valve  faces,'  etc. ,  to  be  heated. 
Suppose  it  takes  a  cubic  foot  of  steam  to  fill  the  cylinder  up  to  the 
point  of  cut-off,  and  20  per  cent,  more,  or  one-fifth  of  a  cubic  foot, 
is  condensed  to  warm  up  the  surfaces. 

Now  suppose  that  instead  of  cutting  off  at  i-4th,  we  cut  off 
at  i -8th,  we  have  nearly  as  much  surface  to  heat  up  as  before,  and 
that  surface  will  be  cooler  on  account  of  the  lesser  temperature  of 
the  cylinder  during  the  greater  expansion,  so  that  we  shall  stiH 
condense  our  one-fifth  of  a  cubic  foot  to  warm  up  the  surfaces,  but, 
having  warmed  them  up,  we  let  only  one-half  a  cubic  foot  through 
to  do  work  and  of  this  half  a  cubic  foot  one-fifth  is  40  per  cent, 
while  it  was  only  20  per  cent,  of  the  cubic  foot  passed  at  quarter 
cut-off.  The  percentage  of  loss  from  cylinder  condensation  thus* 
increases  very  rapidly  with  earjy  cut-offs,  and  more  than  equals  the 
gain  from  increased  expansion.  Experiments  show  that  for  simple 
engines  at  about  80  pounds  pressure  the  least  amount  of  steam  will 
be  required  per  horse- power  when  the  cut-off  takes  place  between 
one-fifth  and  one-quarter  stroke. 

If  you-  will  consult  a  steam  table  you  will  find  that  a  pound  of 
steam  at  80  pounds  gage,  or  say  95  pounds  absolute  pressure, 
contains  1180.7  heat  units.  A  pound  of  steam  of  120  pounds  gage 
or  135  pounds  absolute  contains  1188.7  heat  units.  In  other 
words,  we  have  only  to  put  1188.7—1180.7  =  8  heat  units  more  into 
a  pound  of  steam  to  increase  its  pressure  from  80  to  1 20.  This  is 
a  very  small  percentage  of  the  heat  used,  but  see  how  much  we 
have  added  to  the  power-producing  possibilities  of  the  steam.  In 
Fig.  6  the  heavy  diagram  represents  the  power  theoretically 
obtainable  from  steam  of  80  pounds  gage  95  absolute,  cut-off  at 
one- quarter  stroke  with  an  absolute  back  pressure  of  3  pounds  cor- 
responding to  a  vacuum  of  24  inches.  If  by  the  addition  of  only  8 
heat  units  per  pound  we  raise  the  pressure  to  1 20  pounds  gage  or 
135  absolute,  we  can  with  the  same  terminal  pressure  and  using  the 
same  amount  of  steam,  add  the  area  A  D  E  B  to  our  diagram  ;  or, 
retaining  our  quarter  cut-off,  we  can  get  out  of  the  same  engine, 


*The  area  of  the  two  heads=!^r     The  stroke  equals  2  diameters,  so 

2 

X  stroke=  —  and  this  multiplied  by  the  circumference  D?r=  —  *-  also. 


8  EFFICIENCY  DUE  TO  HIGH  PRESSURE. 

the  greater  power  represented  by  the  diagram  D  F  G  HI.  In 
this  case  we  take  the  same  initial :  volume  as  with  the  80  pound 
steam,  but  the  weight  per  stroke  is  greater  on  account  of  the 
greater  density  of  the  higher  pressure.  The  range  in  temperature 
between  the  initial  and  exhaust  has  been  increased,  but  having 
warmed  the  surfaces  we  can  get  through  the  volume  which  they 
enclose  a  larger  amount  of  steam  on  account  of  the  greater  density 
and  this  greater  weight  of  steam  developing  a  greater  number  of 
horse-power  the  condensation  per  horse-power  is  reduced.  If  we 
carry  back  our  cut-off  to  E  we  greatly  reduce  the  additional  power 
from  the  higher  pressure,  and' with  the  increased  range  of  tempera- 
tures make  a  less  saving  on  the  condensation  per  unit  of  power 
produced. 

In  raising  the  initial  pressure,  however,  with  the  same  ratio  of 
expansion  the  terminal  pressure  is  also  raised.  With  95  pounds 
absolute  and  a  ratio  of  expansion  of  4  we  get  a  terminal  pressure 
of  9514-4=23.75  pounds.  With  an  initial  of  135  and  the  same  ratio 
of  expansion  we  get  a  terminal  of  135-4-4=33.75  pounds,  and  the 
loss  by  free  expansion  is  raised  from  the  area  included  between  the 
line  Cy  and  the  back  pressure  line,  to  the  area  between  the  line 
G  Z  and  the  same  back  pressure  line,  which  latter  area  would  be 
considerably  longer  as  well  as  higher.  It  is  not  so  very  long  ago 
that  engines  were  run  with  initial  pressures  as  low  as  this  new 
terminal  pressure.  When  William  Coutie  started  his  engine  works 
at  Troy,  N.  Y.,  he  made  a  contract  with  a  neighbor  who  was 
running  a  non- condensing  engine  whereby  he  was  entitled  to  the 
use  of  the  exhaust  steam.  He  turned  this  exhaust  steam  into  his. 
own  engine  at  about  atmospheric  pressure,  connected  his  engine  to 
a  condenser  and  ran  his  shop  with  his  neighbor's  exhaust  for 
several  years.  When  the  stroke  is  completed  in  Fig.  6  we  have  a 
cylinder  full  of  steam  at  considerably  above  atmospheric  pressure. 
Instead  of  exhausting  it  into  the  atmosphere  or  the  condenser, 
suppose  we  complete  its  expansion  in  another  cylinder.  We  shall 
then  have  a  compound  engine. 

In  D  F  G  H  /of  Fig.  7  we  have  the  corresponding  diagram 
of  Fig.  6  reduced  for  convenience  to  half  its  length  without  chang- 
ing its  vertical  scale,  just  as  though  the  reducing  motion  had 
been  shortened  one- half.  At  the  end  of  the  forward  stroke  we 
have  in  the  cylinder  a  mass  of  steam  of  a  volume  proportional  to 
the  length  of  the  line  J  G  and  a  pressure  proportional  to  the 


USE  OF   TWO   CYLINDERS  TO  COMPLETE  EXPANSION.  9 

height  of  the  same  line.  This  steam  has  been  expanded  to  four 
times  its  original  volume  in  the  first  cylinder.  Suppose  we  con- 
clude to  expand  it  to  four  times  its  present  bulk  in  another 
cylinder.  Then  the  volume  of  the  second  or  low  pressure  cylinder 
must  be  four  times  the  volume  of  the  first,  for  at  each  stroke  the 
first  cylinder  empties  its  own  volume  into  the  low  pressure  cylinder, 
or  .into  the  receiver  from  which  it  takes  its  steam,  and  the  low 
pressure  cylinder  must  take  this  volume  and  expand,  it  to  four 
times  its  present  size.  The  diagram  in  the  low  pressure  cylinder 
would  be  J  G  C  E  I.  The  combined  effect  so  far  as  the 


FIG.  7. 

expansion  is  concerned  is  the  same  as  though  we  had  cut  off  in 
a  single  cylinder  at  one  -  sixteenth  of  the  stroke,  making  the 
diagram  D  F  C  E  I.  We  have  reduced  the  range  of  temperature 
in  the  first  cylinder  by  raising  the  exhaust  temperature  from  1 10° 
to  256°,  and  we  have  made  the  distribution  of  pressure  much 
more  uniform  through  the  stroke.  Steam  of  135  pounds  admitted 
against  a  piston  having  but  three  pounds  on  the  other  side  would 
occasion  quite  a  shock,  and  if  this  pressure  was  continued  but  for 
one-sixteenth  of  the  stroke,  and  fell  away  as  rapidly  as  the  line 
F  G  C  shows,  the  greater  portion  of  the  stroke  would  be  exe- 
cuted with  comparatively'  low  pressure,  and  the  effort  on  the 


,0  TOTAL   RATIO  OF   EXPANSION. 

crank-pin  would  be  very  jerky.  By  maintaining  a  back  pressure 
of  33  75  pounds  on  the  high  pressure  piston  we  reduce  the  un^ 
balanced  thrust  during  the  first  part  of  the  stroke  ;  by  maintaining 
the  initial  pressure  for  a  quarter  stroke  we  get  no  greater  variation 
of  effort  than  with  the  ordinary  engine,  and  by  setting  the  cranks 
of  the  two  cylinders  at  right  angles  we  can  greatly  increase  the 
uniformity  of  rotative  effort  in  the  shaft.  We  have,  moreover, 
expanded  the  steam  to  135-1 6=8  rV  pounds,  lower  than  we  got 
even  the  80  pound  steam  in  the  simple  engine,  and  this  without 
going  below  a  quarter  cut-off,  and  with  a  less  difference  between 
the  maximum  and  minimum  temperatures  in  either  cylinder. 


FIG.  8. 


Notice  that  the  total  ratio  of  expansion  is  the  volume  of  the 
low  pressure  cylinder  divided  by  the  volume  of  the  high  pressure 
up  to  cut-off.  For  each  stroke  the  high  pressure  cylinder  meters 
off  a  certain  volume  of  steam  ;  this  is  the  initial  volume.  What- 
ever we  may  do  to  it  in  the  meantime  it  will  eventually  occupy  the 
entire  volume  of  the  low  pressure  cylinder,  and  the  final  volume 
divided  by  the  initial  volume  gives  you  your  total  ratio  of  ex- 
pansion. This  makes  it  plain  that  the  cut-off  on  the  low  pres- 
sure cylinder  has  no  influence  on  the  ratio  of  expansion  or  the 
number  of  times  -the  steam  is  expanded.  All  that  the  cut-off 
on  the  low  pressure  cylinder  can  do  is  to  regulate  the  receiver 


CUT-OFF   IN   LOW   PRESSURE  CYLINDER.  II 

pressure.  The  low  pressure  cylinder  has  to  take  away  as  much 
steam  as  the  high  pressure  xcylinder  delivers,  stroke  by  stroke, 
and  it  will  do  it  whether  the  cut-off  is  long  or  short. 

If  you  want  your  high  pressure  diagram  to  end  in  a  point  as 
nt  C.  Fig.  7,  the  low  pressure  cylinder  must  cut  off  when  the 
volume  of  steam  admitted  just  equals  the  volume  of  the  high 
pressure  cylinder.  If  you  lengthen  the  cut-off  so  as  to  take  away 
each  stroke  a  greater  volume  than  the  high  pressure  cylinder 
delivers,  the  delivered  steam  will  expand  into  the  greater  space 
afforded  with  a  consequent  reduction  of  pressure.  Ff,  for  instance, 
the  low  pressure  cylinder  cut  off  at  three-eighths  as  in  Fig.  8r 
instead  of  at  one-quarter  as  in  Fig.  7.  each  volume  J  G  expelled 


FIG.  9 

from  the  high  pressure  cylindei  would  find  a  space  proportional 
to  L  K  to  receive  it.  and  would  expand  to  that  volume  with  the 
reduction  of  pressure  shown.  This  would  reduce  the  back  pres- 
sure on  the  high  pressure  piston,  and  the  initial  on  the  low  (that 
is  the  receiver  pressure)  and  cause  the  loss  of  a  little  shaded 
triangular  area.  It,  on  the  other  hand,  we  cut  off  at  one-eighth  of 
the  stroke,  as  in  Fig.  9.  the  cylinderful  of  steam  which  comes  from 
the  high  pressure  cylinder  has  to  be  compressed  into  a  space  less 
than  its  own  volume,  with  a  consequent  increase  in  pressure, 
raising  the  receiver  pressure  to  K  L,  Fig.  9,  and  making  a 
loop  upon  the  high  pressure  diagram,  such  as  we  get  on  a 
non-condensing  engine  when  the  expansion  is  carried  below  the 


I2  HCC*'  TO   COMPUTE  THE  TOTAL   EXPANSIONS 

atmospheric  pressure.  The  area  of  this  loop  is  represented  by  the 
black  portion  in  Fig.  9.  It  represents  back  pressure  or  negative 
work  and  is  equivalent  to  the  loss  of  an  equal  amount  of  area  inside 
the  diagram.  You  see  then  that  changing  the  point  of  cut-oft  in 
the  low  pressure  cylinder  simply  changes  the  receiver  pressure,  and 
determines  the  apportionment  of  the  load  between  the  cylinders, 
and  you  will  notice  the  paradoxical  fact  that  the  earlier- the  cut-off 
in  the  low  pressure  cylinder  the  greater  the  amount  of  work  which 
that  cylinder  does. 

The  total  -ratio  of  expansion  is  the  ratio  of  expansion  in  the 
high  pressure  cylinder  multiplied  by  the  cylinder  ratio.  By  the 
'cylinder  ratio  I  mean  the  quotient  of  the  volume  of  the  low  pressure 
cylinder  divided  by  the  volume  of  the  high.  For  equal  strokes 
these  volumes  will  be  as  the  squares  of  the  diameters-  and  the 
cylinder  ratio  will  be  the  square  of  the  quotient  of  the  diameter  of 
the  low  pressure  divided  by  the  diameter  of  the  high.  For  instance, 
if  you  have  cylinders  24  and  48  inches  in  diameter  with  the  same 
stroke  the  cylinder  ratio  will  be 

48-1-24=2  and  2x2=4. 

If  the  cylinders  were  24  and  60  'the  ratio  would  be 
60-^24=2.5  and  2.5x2.5=6.25. 

In  Fig.  7  we  had  a  cylinder  ratio  of  four.  The  steam,  having 
been  expanded  four  times  in  the  high  pressure  cylinder,  was  ex- 
panded four  times  more  in  the  low.  It  is  a  common  error  to,'*ake 
the  sum  of  the  expansions  in  the  two  cylinders  as  the  total  expan- 
sion instead  of  their  product.  It  is  a  natural  mistake  to  say  that, 
having  expanded  four  times  in  one  cylinder  and  four  in  another, 
you  have  expanded  4+4=8  times  in  all,  but  this  is  not  so,  because 
the  initial  volume  which  you  expand  in  the  second  cylinder  is  the 
already  expanded  volume  from  the  first.  Fig.  10  will  make  this 
plain.  We  start  with  a  volume  of  steam  represented  by  the  blad< 
square,  and  in  the  high  pressure  cylinder  expand  it  to  four 
times  its  original  volume  as  represented  by  the  rectangle  A  D  CD. 
In  the  low  pressure  cylinder  we  expand  this  larger  volume  A  B  CD 
to  four  times  its  size,  represented  by  A  B  F  E,  and  the  final 
volume  is  16,  not  8,  times  the  original.  The  total  ratio  of  expan- 
sion then  is  the  ratio  of  expansion  in  the  high  pressuie  cylinder 
multiplied  by  the  cylinder  ratio.  Do  not  make  the  mistake  of 
multiplying  by  the  ratio  of  expansion  as  determined  by  the  cut-off 
in  the  low.  The  terminal  pressure  and  total  ratio  of  expansion  is 


MEA.N   PRESSURE   REFERRED  TO   LOW   PRESSURE  CYLINDERS.  13 

the  same  in  Figs.  7,  8  and  9,  notwithstanding  the  wide  difference 
in  the  low  pressure  cut-off.  The  real  ratio  of  expansion  in  the  low 
pressure  cylinder,  that  is  the  continuation  of  the  expansion  from 
the  terminal  in  the  high,  is  the  cylinder  ratio,  because  that  tells 
how  much  bigger  the  volume  of  steam  is  at  the  end  of  the  low 
pressure  than  at  the  end  of  the  high  pressure  stroke. 

I  want  to  make  plain  to  you  the  fact  that  the  mean  effective 
pressure  due  to  the  tptal  ratio  of  expansion  represents  the  total 
horse-power  of  the  engine  when  considered  as  acting  on  the  low 
pressure  piston  alone. 

Suppose,  as  in  the  previous  illustration,  we  have  an  initial 


FIG.  10. 

pressure  of  120  pounds  absolute,  and  a  cylinder  ratio  of  4,  that  is, 
that  the  volume  of  the  low  pressure  cylinder  is  four  times  that  of 
the  high.  Suppose  further  that  the  cut-off  in  the*  high  pressure 
cylinder  is  at  quarter- stroke.  A  quarter  stroke,  or  with  a  ratio 
of  expansion  of  4,  the  mean  pressure  per  pound  of  initial  is 
•  59658*.  The  mean  pressure  in  the  first  cylinder  would  be  then 
1 20x-  59658=7 1. 5896  pounds.  The  back  pressure  equals  the 
terminal  pressure  in  this  cylinder,  and  would  be  1 20-^4=30  pounds. 
Remember  we  are  dealing  with  absolute  pressures  all  the  time1,  and 
the  mean  effective  pressure  would  be  the  mean  pressure  minus  the 
back  pressure=7 1. 5896— 30=41.5896  pounds. 

*See  table  page  5,  POWER,  July,  1895,  or  page  122  "  The  Steam  Engine 
Indicator." 


REDUCING  THE  HIGH   PRESSURE  DIAGRAM. 


120 


HIGH  PRESSURE 


FIG.  ii. 


The  conventional  diagram  which  would  be  made  is  shown  in 
Fig.  n. 

Since  the  low  pressure  cylinder  has  four  times  the  volume  of 
the  high,  it  should  cut  off  at  one-fourth  to  take  the  same  volume 
of  steam  that  the  high  pressure  delivers,  and  continue  the  ex- 
pansion without  loop  or  drop.  Here  again  the  ratio  of  expansion 
is  4,  the  mean  pressure  per  pound  of  initial  .59659  the  initial  30, 
giving  a  mean  pressure  of 
3<>X.59658=i7.8974  pounds. 
Subtract  from  this  say,  three 
pounds  absolute  back  pres- 
sure, giving  14.8974  pounds 
of  mean  effective.  Fig.  12 
gives  the  conventional  dia- 
gram. Now  the  41.5896 
pounds  in  the  high  pressure 
cylinder  will  do  only  one- 
quarter  as  much  work  as 

though  it  acted  in  the  low,  because  the  cylinder  is  only  one-quarter 
the  size.  To  find  the  pressure  which  acting  in  the  low  would  do  an 
equal  amount  of  work  we  must  divide  by  4  and 

41.5896-4=10.3974 

and  the  total  work  is  the  same  as  though  10.3974+14.8974= 
25. 2958  pounds  acted  only  in  the  low  pressure  cylinder. 

In  these  diagrams  you  know  the  length  is  proportional  to 
the  volume,  and  as  in  a  single  cylinder,  the  volume  is  proportional  to 

the  stroke,  the  length  of  the 
diagram  represents  also  the 
length  of  the  stroke.  When 
we  wish  to  compare  two 
diagrams,  however,  they 
must  be  reduced  not  only 
to  the  same  vertical  or  spring  scale,  but  to  the  same  scale  of 
volumes.  Having  been  -expanded  four  times  in  the  high  pressure 
cylinder  and  four  times  in  the  low,  the  volume  at  the  end  of  the 
low  pressure  stroke  will  be  4x4=16  times  that  at  cut-off  in  the 
high.  If  the  length  of  the  low  pressure  diagram  represents  sixteen 
volumes  the  length  of  the  high  pressure  diagram  can  represent  but 
four,  because  the  volume  at  the  end  of  the  high  pressure  stroke 
was  only  four  times  that  at  cut-off.  To  make  it  comparable  with 


LOW  PRESSURE 


FIG.  12. 


THE   COMBINED   DIAGRAM. 


the  low  pressure  diagram  we  must  reduce  it  to  one-quarter  of  its 
length,  keeping  the  same  vertical  scale,  as  shown  by  the  dotted 
diagram  in  Fig.  n.  In  doing  this  we  divide  its  area,  which  is 
proportional  to  the  power  it  representb,  by  4,  which  is  just  what  we 
did  when  figuring  the  power  above.  This  diagram  can  now  be 
placed  upon  the  low  pressure  diagram  as  shown  in  Fig.  13,  and 
the  combination  represents  the  action  of  the  steam  with  the  total 
ratio  of  expansion  16,  and  its  area  is  proportional  to  the  power 
developed  when  the  mean  effective  pressure  represented  by  that 
area  is  considered  as  acting  on  the  low  pressure  piston.  The  mean 
pressure  per  pound  of  initial  for  16  expansions  is  .23579  and 

1 2ox-  23579-3=25. 2948 
as  before. 

Another  way  of  looking  at  it  is  this  :  To  find  the  mean  effec- 
tive pressure  of  a  diagram,  you  multiply  its  area  by  the  scale  of  the 
spring  and  divide  by  the  length.  In  the  combined  diagram  the 
area  of  the  high  pressure 
portion  would  by  this  proc- 
ess be  divided  by  16  instead 
of  by  4,  which  is  equivalent 
to  dividing  its  mean  effec- 
tive considered  with  refer- 
ence to  the  cylinder  in 
which  it  was  first  expanded 
by  4.  In  combining  dia- 
grams thus  the  length  of 
the  low  pressure  diagram 
must  equal  that  of  the  high 
multiplied  by  the  cylinder 
ratio.  It  is  usually  easier  to  reduce  the  high  pressure  cylinder  in 
this  proportion  than  to  lengthen  the  low. 

We  have  seen  that  in  the  simple  engine  it  does  not  do  to 
expand  until  the  terminal  equals  the  back  pressure.  With  a  com- 
pound engine  we  can  carry  the  expansion  much  further  than  in  a 
simple  engine,  and  if  we  could  profitably  bring  the  combined 
diagram  to  a  point  in  all  cases,  the  question  of  compound  engine 
design  would  be  much  simplified.  Suppose  again  that  we  have 
1 20  pounds  gage=i35  absolute  initial  and  run  non-condensing, 
exhausting  at  15  pounds  absolute  Then  in  order  that  the  terminal 
pressure  may  equal  the  back  pressure  we  must  expand  135-^-15= 


FIG.  13. 


16  DIVIDING  DIAGRAM  FOR  EQUAL  WORK. 

9  times.  The  diagram  is  shown  in  Fig.  14.  How  shall  we  divide 
it  lip  between  the  high  and  the  low  pressure  cylinder?  The  usual 
object  is  to  divide  the  work  equally  between  the  two.  This  will  be 
done  by  dividing  the  diagram  into  equal  areas,  by  a  line  like  CD 
so  located  that  the  area  above  it  representing  the  high  pressure 
diagram  will  equal  the  area  of  the  low  pressure  diagram  below  it. 
Where  both  diagrams  end-  in  a  point,  as  in  the  case  under  consid- 
eration, this  will  occur  when  the  ratio  of"  expansion  is  the  same  in 
both  cylinders,  that  is  when  CD  is  just  as  many  times  as  long  as 
AB  and  £Fis  as  long  as  CD.  In  Fig.  14,  for  instance,  CD  is 
3  times  as  long  as  A  B  and  £Fis  3  times  as  long  as  CD.  This 
is  accomplished  by  making  the  ratio  between  the  cylinders  the 
square  root  of  the  total  ratio  of  expansion.  To  get  equal  work 
und^r  these  conditions  we  must  have  equal 
expansions  in  the  two  cylinders.  The  total 
expansions  will  be  the  product  of  those  in  the 
two  cylinders,  then  obviously  the  expansion 
in  each  will  be  the  square  root  of  the  whole, 
and  since  the  expansion  in  the  low  is  the 
cylinder  ratio,  the  cylinder  ratio  is  the  square 
root  of  the  total  ratio  of  expansion,  or  in 
this  case,  of  the  initial  divided  by  the  back 
pressure.  Notice  that  in  all  these  diagrams 
the  length  of  the  line  EF divided  by  .the  line 
CD  is  the  cylinder  ratio,  and  you  cannot 
change  the' length  of  the 
high  pressure  part  of  the 
diagram  without  changing 
the  ratio  between  your 
=-_F  cyHnder  volumes^ 

Now  with  an  engine 
^__x  proportioned  on  these 
lines  suppose  the  load  to 
increase  and  steam  to  be 
carried  one-half  instead  of 

one-third  stroke.  Either  of  three  things  may  happen,  according 
to  how  we  manage  the  low  pressure  cut-off.  If  we  have  a  fixed 
<:ut-off  at  one-third  stroke,  the  receiver  pressure  will  go  up  to  the 
terminal  in  the  high  pressure  cylinder,  as  indicated  by  CD,  Fig.  15, 
making  the  high  pressure  diagram  still  end  in  a  point,  but  dis- 


EFFECT  OF  VARIABLE  LOAD. 


turbing  the  balance  of  the  load,  much  more  of  the  work  being  on 
the  low  pressure  than  upon  the  high.  To  make  the  low  pres- 
sure cut-off  earlier  would  add  to  the  evil.  Suppose  we  extend 
the  cut-off  in  the  low  pressure  cylinder  to  the  same  extent  as  that 
in  the  high,  cutting  off  at  one-half  in  both,  as  in  Fig.  15.  The 
receiver  pressure  will  then  remain  constant  and  the  load  will  re- 
main equally  distributed  between  the  cylinders.  The  high  pres- 
sure cylinder  no  longer  ends  in  a  point,  but  there  is  some  loss 
from  free  expansion  in  the  receiver  as  at  A.  This,  however,  is 
just  eqital  to  the  loss  from  free  expansion  at  B.  So  that  so  long 
«s  the  ratio  between  the  cylinders  is  the  square  root  of  the  quotient 
of  the  absolute  initial  divided  by  the.  absolute  back  pressure,  the 
load  will  remain  equally  distributed  between  the  cylinders  if  we 
vary  the  cut-offs  equally,  no  matter  how  the  load  may  vary.* 
You  will  notice  one  thing,  that  if  we  proportion  our  cylinder  ratio 
to  keep  the  expansion  curve  smooth  at  a  given  load,  we  have 
either  got  to  lose  some  area  from  the  theoretical  diagram  by  free 
expansion  when  more  load  comes  on,  as  at  A  in  Fig.  15,  or  by 

running  the  receiver  pressure 
up  to  the  terminal  in  the-  high 
pressure  cylinder,  to  throw  a 
disproportionate  part  of  the 
load  on  the  low  pressure  cylin- 
der. The  designer  of  a  pump- 
ing or  marine  engine  where 
the  point  of  cut-off  in  tHe  first 
cylinder  is  fixed,  can  simply 
determine  upon  the  total  num- 
ber of  expansions  he  wants  to 
.  •  employ,  lay  out  his  theoretical 
combined  diagram,  locate  the 
line  CD  where  it  will,  divide 
the  load  between  the  cylinders 
as  he  wishes  it  divided,  and 

his  problem  is  solved.  But  a  stationary  engine  subjected  to 
varying  loads  must  change  the  point  of  cut-off  in  the  first 
cylinder  in  order  to  control  the  speed.  If  we  have  fixed  the 
cylinder  ratio  to  give  a  smooth  expansion  curve  and  equal 

*See  A  Methbd  of  Proportioning  the  Cylinder  of  Compound  Engine,  by 
E..C.  Knapp,  Trans.  Amer.  Soc.  Mech.  Engrs.,  Vol.  XVI. 


FIG.  15. 


THE   TERMINAL   PRESSURE. 


distribution  of  load  at  one  total  ratio  of  expansion,  the  same 
cylinder  ratio  will  not  harmonize  them  at  any  other  ratio  of 
expansion.  We  i  jst,  therefore,  determine  ratio  of  total  expan- 
sion we  will  use  at  average  load,  and  make  our  engine  large 
enough  to  develop  the  average  load  with  the  mean  effective  that 
we  can  realize  with  the  given  initial  and  ratio  of  expansion.  We 
can  then  arrange  our  cylinder  ratio  to  give  equal  loads  at  this 
point  of  cut-off  if  we  desire,  or  to  have  a  smooth  expansion  line  or 
a  drop  in  the  first  cylinder  as  may  seem  best. 

Theoretically,  at  least,  the  'engine  will  require  the  least 
amount  of  steam  per  indicated  horse-power  when  the  actual  indi- 
cator diagrams  taken  from  the  cylinders  combined,  as  in  Eig.  13, 
most  nearly  fill  the  area  of  the  theoretical  diagram.  We  shall  get 
the  same  losses  of  area  here  as  with  the  simple  engine,  from  a 
failure  to  realize  the  full  boiler  pressure  in  the  high  pressure  cylin- 
der, froip  the  steam  line  falling  off,  from  rounded  corners  and 
from  back  pressure  ;  also  in  the  low  pressure  cylinder  from  a  fail- 
ure to  realize  as  initial  the  full  receiver  pressure.  In  addition  we 
may  lose  by  free  expansion  in  the  receiver  as  at  Fig.  8,  or  by  loop- 
ing the  high  pressure  diagram  as  at  Fig.  9.  Just  as  soon  as  a 
certain  point  of  cut-off  in  the  high  pressure  cylinder  is  exceeded, 
the  terminal  in  the  low  pressure  will  exceed  the  line  of  counter 
pressure,  and  there  will  be  a  theoretical  loss  there  by  free  expan- 
sion analogous  to  that  in  the  simple  diagram  shown  in  Figs.  3  and  4, 

This  terminal  pressure  will  be  just  the  same  whatever  the  point 
of  cut-off  in  the  low  pressure  cylinder,  and  ther6  is  no  way  of 
dividing  it  between  the  cylinders.  We  may,  as.  in  Figs.  14  and  15, 
so  proportion  the  cylinders  that  there  will  always  come  to  the  high 
pressure  cylinder  a  loss  by  free  expansion  equal  to  the  loss  upon 
the  low  pressure  cylinder  from  the  same  cause,  but  this  will  be 
in  addition  to  the  loss  at  the  low  pressure  cylindes,  and  will  not 
lessen  it  at  all.  It  simply  keeps  the  load  between'  the  cylinders 
equal,  and  since  with  anything  but  a  constant  load  we  must  have 
free  expansion  in  the  receiver,  it  may  be  arranged  as  described 
above  to  vary  equally.  If  the  loss  by  receiver  expansion  or  "drop,  '  ' 
as  it  is  usually  called,  is  serious,  we  want  to  so  proportion  our 
cylinders  that  the  drop  shall  be  least  at  the  load  at  which  the 
engine  runs  most  of  the  time.  The  diagram  shown  in  Fig.  14  must 
represent  the  minimum  work  of  the  engine,  for  if  the  'cut-off 
were  any  shorter  the  low  pressure  diagram  would  loop.  Ait 


SUMMARY.  19 

engine  designed  on  these  lines  then  would  have  some  drop  when 
running  at  anything  above  its  minimum  load.  If,  instead  of  pro- 
portioning the  cylinders  by  the  rule  there  given,  i.  e. ,  the  cylinder 
ratio  equals  the  square  root  of  the  quotient  of  the  initial  divided  by 
the  back  pressure,  we  lay  out  a  theoretical  diagram  with  the  num- 
ber ol  expansions  which  we  want  to  use  at  the  average  load,  or  the 
most  frequent  load,  and  then  draw  a  horizontal  line  dividing  its  area 
equally,  we  shall  have  an  equal  division  of  work  with  no  drop  at 
the  load  at  which  the  engine  is  most  used,  but  the  load  would  not 
remain  evenly  balanced  when  the  low  pressure  cut-off  was  varied 
the  same  as  the  high. 

From  what  has  been  said  I  would  like  you  to  catch  and  to 
remember  particularly 

First. — That  the  total  ratio  of  expansion — that  is,  the  total 
number  of  times  the  steam  is  expanded — is  the  ratio  of  expansion 
in  the  high  pressure  cylinder  multiplied  by  the  cylinder  ratio. 

Second. — That  this  expansion  may  be  effected  in  three  ways. 

a.  In  the  high  pressure  cylinder 

b.  In  the  receiver. 

c.  In  the  low  pressure  cylinder. 

Third. — That  changing  the  point  of  cut-off  in  the  low  pressure 
cylinder  does  not  affect  the  work  done  by  the  engine  as  a  whole, 
nor  even  the  terminal  pressure  in  that  cylinder. 

Fourth. — Shortening  the  cut-off  in  the  low  pressure  cylinder 
raises  the  receiver  pressure  and  throws  more  of  the  load  on  the  low 
pressure  cylinder 

Fifth. — Lengthening  the  cut-off  on  the  low  pressure  cylinder 
lowers  the  receiver  pressure  and  throws  load  off  from  the  low 
pressure  cylinder  onto  the  high. 

Sixth. — When  the  cut-off  on  the  low  pressure  cylinder  is  fixed 
the  receiver  pressure  will  vary  with  the  cut  off  in  the  high  pressure 
cylinder,  and  the  greater  the  load  the  greater  the  proportion  of  it 
which  the  low  pressure  cylinder  will  carry. 

Seventh. — When  the  cut-ofi  on  the  low  pressure  cylinder 
vanes  the  same  as  that  on  the  high  the  receiver  pressure  will  be 
constant,  and  the  load  remain  more  evenly  distributed. 

Eighth  — When  there  is  no  drop  the  cut-ofi  in  the  low  pres- 
sure cylinder  must  be  the  reciprocal  of  the  cylinder  ratio;  i.  e.,iJ 
th«  cylinder  ratio  is  4  the  cut-off  in  the  low  pressure  cylinder  must 
be  one-fourth,  etc 


20  TOTAL  EXPANSIONS  ADVISABLE. 

You  see,  too,  that  the  best  ratio  between  the  cylinders  de- 
pends to  a  great  extent  upon  the  total  number  of  expansions  we 
desire  to  effect,  which  will  depend  upon  the  boiler  pressure,  the 
back  pressure,  the  character  of  the  engine  and  the  use  to  which  it 
is  to  be  applied.  Considering  the  question  only  from  the  stand- 
point of  steam  efficiency  there  is  a  wide  difference  in  opinion  as  to 
the  number  of  expansions  which  with  a  given  set  of  conditions  will 
produce  a  horse-power  with  the  consumption  of  the  least  amount  of 
steam. 

^B.  F.  Isherwood,  in  an  exhaustive  review  of  a  compound 
engine  test  in  the  Jour  Franklin  Inst.  for  October,  1885,  points 
out,  page  268,  that  the  heat  units  consumed  per  hour  per  horse- 
power were  almost  identical,  and  that  no  economy  of  fuel  followed 
increasing  the  measure  of  expansion  with  which  the  steam  was  used 
from  6. 26  to  9.64  times.  It  was  a  slide  valve  engine  approximately 
ii  and  19  by  19  with  about  90  pounds  pressure,  run  condensing 
and  partially  steam  jacketed. 

Dr.  C.  E.  Emery  deduces  from  the  results  of  his  experiments 
with  the  U.  S.  Revenue  steamers  that  the  most  economical  ratio  of 
expansion  of  steam  in  two-cylinder  compound  engines  where  the 
pressure  varies  from  75  to  79  pounds  absolute  is 

22  -f.  abs.  initial  pressure 
ratio  of  expansion  =•  — • 

Dr.  Thurston,  in  his  Manual  of  the  Steam  Engine,  Part  i, 
page  596,  says  :  ' '  The  first  step  m  designing  the  compound  engine 
is  the  determination  of  the  best  ratio  of  expansion  under  the 
assumed  conditions  of  operation  and  for  a  given  type  of  engine,  for 
a  single  cylinder  •  then  the  best  ratio  of  expansion  for  the  series  ; 

*  *  *  *  The  extent  of  economical  expansion  in 
a  single  cylinder  will  vary  with  the  working  range  of  temperature 
and  pressure  and  with  the  physical  condition  of  rhe  working'  fluid, 
but  it  may  be  taken  as  determined  by  experience  as  perhaps  not 
above  two  and  a  half  expansions  for  unjacketed  engines  with  wet 
steam  or  not  over  three  or  four  for  good  practice  with-  the  better 
class  of  engines.  The  total  expansion  ratio  thus  becomes  for  the 
several  types  of  multiple- cylinder  engines  as  btlow  : 


No.  of  Cylinders  
Ratio  of  expansion  ' 

i 

2  S  tO  % 

2 

6.2=;  to  a 

1  6  to  27 

40  to  81 

Initial  pressure  

21  to  v)  IDS 

I2O  tO  3OO 

ISO  tO  8<3O 

TOTAL   EXPANSIONS  ADVISABLE.  21 

The  Pawtucket  pumping  engine  tested  by  Prof.  J.  E.  Denton 
gave  a  horse  power  on  13.47  pounds  of  steam  per  hour  with  127 
pounds  boiler  pressure,  27.9  inches  vacuum  and  16  expansions. 
The  ferry  boat  Bremen,  witji  98  pounds  boiler  pressure,  26.4 
inches  of  vacuum  and  ten  expansions,  required  18.  i.  A  Wheelock 
tripW  expansion  engine  tested  by  Mr.  Rockwood,  when  running 
as  a  compound  with  the  middle  cylinder  cut  out  required  only 
12.9  pounds  of  steam  per  hour  with  142  pounds  boiler  pressure 
condensing,  and-about  25  expansions.  (Trans.  A.  S.  M.  E.,  vol. 

XIII,  page  656.) 

Prof.  R.  C.  Carpenter  tested,  a  100  horse-power  McEwen 
engine  at  112  pounds  boiler  pressure,  22  inches  vacuum,  steam 
jacketed,  and  found  the  lowest  steam  consumption  between  9  and 
vS total  expansions.  (Trans.  A.  S.  M.  E..  vol.  XIV,  p.  426.) 

Mr.  F.  H.  Ball  thinks  that  with  150  potinds  pressure  and  a 
good  vacuum  at  least  32  expansions  should  .be  realized  in  a  triple 
expansion  engine.  (Trans.  A.  S.  M.  E.,  vol.  XV,  page  776.) 

The  North  Point,  Milwaukee,  triple  expansion  pumping  en- 
gine used  19.55  expansions  with  121.45  pounds  initial  pressure, 
13.84  pounds  vacuum,  while. making  its  record- making  run  on 
11.678  pounds  of  dry  steam  per  hour  per  horse-power.  (Trans. 
A.  5.  M.  E.,  vol.  XV',  page  377.) 

The  Laketon,  Indiana,  pumping  engine  tested  by  Prof.  J. 
E.  Denton,  used  13.5  pounds  of  dry  steam  per  hour  at  150  pounds 
boiler  pressure  and  20  expansions.  (Trans.  A.  S.  M.  E.,  vol. 

XIV,  page  1371.) 

A  Sulzer  triple  expansion  Corliss  engine  in  Germany  does 
a  horse-power,  on  12.73  pounds  of  feed  water  per  hour  with  24 
expansions.  "The  foregoing  results,  as  a  whole,  support  the 
theory,"  Prof.  Denton  says,  in  reporting  this  test,  "that  with 
condensing  engines  up  to  at  least  24  expansions  the  economy 
increases  with  increase  in  the  ratio  of  expansion." 

Mr.  John  T.  Hen  thorn,  reports  a  triple  expansion  with  128 
pounds  boiler  pressure,  26.5  inches  vacuum,  16  expansions,  12.9 
pounds  of  steam  per  hour  per  horse-power. 

Another  triple  in  an  iron  works  with  145  pounds  boiler  pres- 
sure, 28  inches  vacuum  and  22  expansions  used  12.6. 

The  real  effect  of  "drop"  in  the  receiver  is  still  a  matter  of 
discussion.  Notwithstanding  there  are  some  designers  who  attach 
little  importance  to  it,  I  think  it  may  safely  be  said  that  no  one 


22  EFFECT  OF   DROP 

considers  it  a  desirable  thing,  and  all  would  like  to  avoid  it  if 
it  could  be  done  without  introducing  more  serious  complications 
and  losses.  It  is  said  that  drop  cannot  be  detrimental  to  economy, 
because  steam  expanding  freely  in  this  way  loses  no  heat,  but 
becomes  superheated,  and  at  the  lower  pressure  contains  every 
unit  of  heat  which  it  contained  at  the  high.  This  would  be  true 
if  the  free  expansion  continued  to  the  back  pressure,  and  the 
receiver  pressure  were  n<x  higher  than  the  back  pressure  in  the 
low  pressure  cylinder.  The  expanded  steam  w6uld  still  contain 
every  unit  of  heat  that  it  had  when  it  entered  the  receiver,  but  it 
could  do  no  work.  It  has  lost  its  "potential,"  as  the  electrical 
men  would  say,  and  however  superheated  it  may  be  it  cannot 
do  any  work.  By  reducing  the  receiver  pressure  it  has  allowed 
the  high  pressure  cylinder  to  do  more  work  (all  the  work,  in  fact), 
but  it  has  reduced  it  to  the  condition  of  a  simple  engine,  its  tem- 
perature ranging  from  the  initial  to  the  ultimate  back  pressure. 
We  might  equally  well  regard  drop  between  the  boiler  and  engine 
as  harmless,  because  the  steam  is  superheated  by  such  drop  or 
throttling.  I  think  we  would  prefer  to  keep  our  expansion  line 
free  from  loops  and  drops  if  we  could.  The  fact  that  we  have 
superheated  steam  for  use  in  the  second  cylinder  does  not  wipe 
out  the  loss  we  have  already  sustained  in  the  first.  The  total 
loss  by  cylinder  condensation  in  a  compound  engine  is  not  the 
sum  of  the  losses  in  the  two  cylinders,  but  only  the  greater  of 
these  losses.  Suppose  that  in  the  high  pressure  cylinder  ten  per 
cent,  of  the  entering  steam  was  condensed  and  passed  through 
as  water.  Before  the  end  of  the  exhaust  stroke  all  this  water 
will  be  re-evaporated  and  the  second  cylinder  will  get  practically 
the  same  quality  of  steam  that  the  first  got.  Let  us  get  this  plain. 
Each  cylinder  must  give  up  to  the  out  going  steam  exactly  as 
much  heat  as  it  takes  out  of  the  incoming  steam.  If  it  gave  up 
any  more  it  would  become  a  refrigerating  machine,  and  if  it  gave 
up  any  less  heat  would  accumulate  in  it  and  melt  it  down,  so  that 
when  the  steam  goes  to  the  receiver  from  the  high  pressure  cylinder 
it  carries  all  the  -heat  that  it  brought  from  the  boiler  with  the 
exception  of  the  small  amount  which  has  been  transformed  into 
work  in  the  high  pressure  cylinder,  as  explained  in  Lecture  i*, 
and  what  has  been  lost  by  radiation.  If  then,  the  loss  through 
initial  condensation  has  been  ten  per  cent. 'in  the  first  cylinder, 
*See  Lecture  on  Heat,  November,  1894,  issue  of  Power. 


USE   OF   THREE   OR    MORE   CYLINDERS. 


and  ten  per  cent,  of  the  same  volume  of  steam  is  similarly  con- 
densed in  the  low,  the  loss  by  cylinder  condensation  in  the  engine 
regarded  as  a  whole  has  been  ten,  not  twenty,  per  cent.  So  that, 
as  Dr.  Thurston  shows  us,*  the  loss  from  this  cause  is  best  avoided 
when  it  is  equally  divided  between  the  cylinders.  Drop  increases 
temperature  range  in  the  first  cylinder  and  the  condensation  that 
we  may  naturally  expect  there,  and  it  is  doubtful  if  we  can  get 
square  by  the  avoidance  of  condensation  in  the  second  cylinder  by 
the  consequent  superheating. 

Suppose  now  we  had  an  initial  pressure  of  175  pounds  gage, 
190  absolute.  To  get  a  terminal  pressure  of  about  7  pounds  we 
should  need  190-5.7=27  (about)  expansions.  This  would  require 
about  5. 2  expansions  in  each  cylinder  if  we  divide  them  equally. 
If  we  use  less  than  5.2  in  one  we  must  use  more  than  5.2  in  the 
other  ;  but  we  have  seen  that  5  expansions  are  too  many  to  use  in 
a  single  cylinder  for  the  best  economy.  Suppose,  then,  we  make 
the  high  pressure  cylinder 
of  such  a  size  that  CD, 
Fig.  1 6,  will  represent  its 
volume,  and  A  B  will  be 
one-third  of  CD.  Now, 
if  QX,  as  before,  repre- 
sents the  volume  of  the 
low  pressure  cylinder,  and 
we  cut  off  in  this  cylinder 
also  at  one-third,  we  shall 
get  the  drop  shown  in  the 
diagram  and  a  wide  range 
of  temperature  in  the  first  cylinder.  This  can  be  avoided  by  put- 
ting in  a  third  or  intermediate  cylinder  to  effect  the  expansion 
from  D  to  F  instead  of  lefting  it  take  place  freely  in  the  receiver. 
This  gives  us  a  triple  expansion  engine.  Mr.  George  I.  Rockwood 
claims  that  it  is  better  to  leave  out  the  middle  cylinder,  using  two 
cylinders  with  a  large  ratio,  and  tolerate  the  drop.f  and  he  has 
•ucceeded  in  producing  some  efficiencies  closely  approaching  those 
of  the  triple  expansion  engine,  with  engines  which  were  practically 
triples  with  the  intermediate  cylinder  left  out  If  it  were  simply  a 

*  Manual  Steam  Engine,  part  L,  p.  594. 

t  Railroad  and  Eng.  Jour.,  Dec.,  1^91.    Trans.  A.  S.  M.  E.,  Vol.  XIII, 
p.  647,  Vol.  XIV,  462. 


FIG.  16. 


24 


THE  RECEIVER. 


question  of  saving  the  triangular  area  the  call  for  the  third  cylinder 
would  be  less  imperative.  If  the  increased  range  of  temperature 
in  the  first  cylinder  induces  excessive  initial  condensation  there, 
which  is  only  partially  recovered  in  the  second  cylinder,  the  inter- 
mediate cylinder  may  be  worth  the  cost  of  installation,  maintenance 
and  complication: 

Now  a  few  words  in  regard  to  the  receiver.  From  the 
inquiries  I  receive  there  appears  to  be  an  impression  that  there  is  a 
certain  fixed  ratio  between  the  volume  of  the  receiver  and  that  of 
the  cylinders.  If  it  were  not  for  the  cost  and  loss  by  radiation  I 
would  say  ' '  the  larger  the  better. ' '  Let  us  study  its  effect,  and 
we  can  better  judge  of  its  required  size.  Suppose,  first,  we  have  a 
pair  of  cylinders  without  any  receiver,  one  exhausting  directly  into 


FIG.  17. 

the  other  as  in  Fig.  17.  .  Suppose  that  when  the  piston  moved 
from  right  to  left  the  steam  was  cut  off  at  quarter  stroke,  making 
the  expansion  line  shown  beneath  the  cylinder.  When  the  exhaust 
valves  are  opened  there  will  be  no  immediate  fall  of  pressure,  for 
the  steam  must  go  into  the  low  pressure  cylinder,  and  that  piston 
has  not  yet  begun  to  move  and  make  room  for  it.  As  the  pistons 
move  to  the  right  the  steam  finds  a  constantly  increasing  space 
with  a  consequent  gradual  decrease  of  pressure,  so  that  the  forward 
pressure  upon  the  large  piston  is  shown  by  the  expansion  line 
beneath  that  cylinder,  and  as  this  is  also  the  back  pressure  in  the 
small  cylinder  we  can  complete  the  diagram  for  the  high  pres- 


EFFECT  OF  RECEIVER.  25 

sure  cylinder  by  transferring  this  line  to  it  as  shown  by  the  line 
E'C.  With  this  arrangement  the  pressure  in  the  high  pressure 
cylinder  goes  away  down  to  the  terminal  in  the  low,  and  the 
entering  high  pressure  steam  finds  a  chilly  reception  ;  not  so  chilly 
as  though  we  had  used  but  one  cylinder  and  got  the  diagram 
A  B  C  E,  but  ^nevertheless  the  range  is  too  high.  If  we  cut  off 
say  at  one-quarter  in  the  low  pressure  cylinder* the  expansion  in 
that  cylinder  will  go  on,  but  we  have  shut  off  the  exhaust  from 
the  high  pressure  cylinder  and  the  back  pressure  line  will  run  up 
along  the  line  F  G. 

In  our  consideration  of  the  engine  we  have  regarded  the  back 
pressure  line  of  the  high  pressure  cylinder  as  practically  straight 
(see  CD  in  Figs.  13,  14,  15,  16).  Here  we  find  it  extremely 
crooked,  as  E  F  G.  If  there  were  no  clearance  the  line  F  G 
would  go  infinitely  high,  for  we  would  be  compressing  three- 
quarters  of  a  cylinderful  of  steam  into  nothing,  but  every  times 
you  double  the  room  into  which  you  compress  it  you  reduce  the 
resultant  pressure  one-half.  Now,  suppose  instead  of  exhausting 
one  cylinder  directly  into  the  other  we  exhaust  it  into  a  receiver. 
Then  when  the  cut-off  in  the  low  pressure  cylinder  occurs  the 
steam  will  continue  to  be  exhausted  into  the  receiver,  but  the 
pressure  will  rise  in  inverse  proportion  to  the  size  of  the  receiver. 
If  the  receiver  were  only  three-quarters  the  size  of  the  high 
pressure  cylinder,  the  pressure  at  G  would  be  double  that  at  F 
because  two  volumes  of  steam,  the  three-quarters  cylinderful 
and  the  equal  volume  in  the  receiver,  would  be  compressed  into 
one.  If,  however,  it  were  ten  times  aS  large  as  the  high  pressure 
cylinder  the  pressure  at  G  would  be  only  10  3-4^.10=1.075 
times  that  at  Ft  and  the  line  would  run  like  F  H,  But  we  should 
never  get  down  to  F,  for  when  the  high  pressure  exhaust  opened 
it  would  find  in  the  receiver  the  steam  of  the  previous  stroke,  and 
would  have -to  exhaust  again  at  that  pressure.  The  low  pressure 
cylinder  takes  out  in  a  quarter  stroke  as  much  steam  as  the  high; 
pressure  delivers  during  the  whole  stroke,  but  the  volume  of 
the  receiver  is  so  large  in  proportion  to  the  amounts  added  to  and 
taken  from  it  tfiat  the  fluctuation  of  pressure  is  not  great.  The 
larger  the  receiver  the  nearer  the  back  pressure  line  of  the  high 
pressure  cylinder  and  the  steam  line  of  the  low  .will  approach  to 
a  straight  line.. 


COMBINING   DIAGRAMS. 


When  a  volume  of  steam  is  taken  from  the.  boiler,  expanded 
a  given  number  of  times  and  exhausted  against  a  given  back 
pressure,  either  above  or  below  that  of  the  atmosphere,  we  can 
make  a  theoretical  diagram  which  will  show  the  ideal  action  of 
the  steam  under  the  assumed  conditions.  Comparing  with  this 
ideal  diagram  the  diagram  actually  obtained,  we  have  in  the  difr 
ference  a  measure  of  the  imperfection  of  the  machine  as  a  work  of 
human  art.  For  instance,  in  Fig.  18  let  vertical  distances  rep- 
resent pressures  and  •  horizontal  distances  volumes.  To  start 
with,  we  have  a  volume  A  B  representing  the  amount  of  steam 
which  under  theoretical  conditions,  that  is  if  the  given  pressure 
could  be  realized  and  maintained,  would  be  contained  in  the  cylin- 
der at  the  >point  of  cut-off,  including  that  in  the  ports  and  clearance 
spaces  below  the  cut-off  valve  ;  in  other  words,  the  volume  of 
steam  shut  into  the  engine,  between  the  piston  and  the  cut-off 
valve  at  the  instant  of  cut-off.  When  the  piston  has  moved  to  C 
this  volume  will  be  doubled  and  its  pressure  halved.  At  this 
distance  from  O  A  then  representing  the  doubled  volume,  set  off 
the  point  C  at  a  height  representing  30  pounds.  When  the  pis- 
Ion  is  at  D  the  volume  will  be  three  times  the  original,  and  the 
pressure  one  third  of  60,  or  20  pounds.  When  the  piston  arrives 
at  E  the  volume  is  four  times  the  original  and  the  pressure  one- 
quarter  or  15  pounds.  Locate  ther  point  E  four  times  as  far 
away  from  (he  vertical  line  O  A  as  is  the  point  B  and  15  pounds 
above  the  line  of  zero  pressure  O  X.  Connecting  the  sepoints 
by  the  curve  B  C  D  E  we  have  a  curve  illustrating  the  relation 
of  volumes  and  pressures  when  the  steam  expands  under  ideal 
conditions.  At  the  end  of  the.  stroke  the  exhaust  valve  should 
open  and  the  pressure  fall  on  the  line  E  F  to  that  of  the  space 
into  which  the  engine  exhausts,  which  we  will  assume  to  be  a 


THE   IDEAL  AND  THE   PRACTICABLE  WORKING  OF  STEAM.  27 

vacuum  of  26  inches,  or  a  pressure  of  2  pounds  absolute.  The 
counter  pressure  should  ideally  continue  constant  along  the  line 
F  G  until  the  admission  of  steam  at  the  end  of  the  backward 
stroke  sends  the  pressure  up  to  60  again-on  the  line  G  A.  We 
have  then  as  the  ideal  diagram  producible  by  a  volume  of  steam 
at  this  pressure  working  through  the  given  expansion  A  B  C  D 
E  F  G.  Comparing  this  with  the  actual  diagram  it  is  seen  that 


FIG.  18. 


all  this  area  has  not  been  realized  in  practice,  but  that  through 
clearance,  failure  to  realize  the  boiler  pressure,  tardiness  of  ex- 
haust, etc.,  a  considerable  proportion  is  lost,  while  on  the  other 
hand  between  D  and  E  the  actual  expansion  line  overruns  the 
theoretical  probably  on  account  of  re-evaporation  at  the  lower 
pressure,  of  heated  water  in  the  cylinder,  as  I  explained  in  the 
lecture  on  Steam. 


28  DRAWING  THE  IDEAL  ON  THE  ACTUAL  DIAGRAM. 

The  ideal  diagram  is  usually  laid  out  on  the  actual  diagram 
itself.  After  the  expansion  line  has  become  well  established 
choose  two  points  on  the  curve  as  /  and  '  C,  and  through  them 


FIG.  19, 

draw  horizontals  and  verticals  to  form  the  rectangle  as  shown. 
Then  draw  the  diagonal  J  O  and  extend  it  until  it  cuts  the  line 
of  absolute  vacuum  or  zero  pressure  O  X  14.7  pounds  below  the 
atmospheric  line.  From  O  erect  O  A  as  the  zero  line  of  volumes 
and  the  space  between  O  A  and  the  actual  diagram  will  repre- 
sent the  clearance.  Then  divide  the  length  of  the  diagram 


FIG.  20'. 


including  the  clearance  as  G  F  into  any  number  of  equal  parts, 
and  lay  out  the  theoretical  curve  as  already  explained,  working 
backwards  to  locate  the  point  B,  of  theoretical,  cut-off  at  boiler 
pressure. 


COMPARING  COMPOUND  DIAGRAMS  WITH   THE  IDEAL.  29 

In  a  compound  engine  we  have  a  volume  of  steam  admitted 
to  the  high  pressure  cylinder  finally  expanded  to  fill  the  entire 
volume  of  the  low  pressure  cylinder  and  exhausted  to  the  con- 


M 

uciisci    ur   d 

plot    very 

uuuBpacrc.      vv  e  can 

simply    the    diagram 

'        \ 

which  would  show  the  ideal  ac- 

110 

\                     tion  of  the 

steam 

with 

the  given 

.  \                    number  of  expansions, 

initial  and 

\                   back 

pressure,  -but  how  shall  we 

100- 

*                   arrange    the  diagrams 

from   the 

\                 t  wo 

cylinders   o  f   a 

compound 

\                to  see  how  nearly 

their  combined 

90" 

\                effect 

approaches  the  ideal  ? 

\                     Suppose,    fo 

r  instance,    we 

80- 

have 

the  two  diagrams  shown  in 

\           FiSs- 

19  and  20 

taken  from  the 

\          high 

and  low  pressure  cylinders 

70 

\       of  an 

engine  in 

which   the  low 

\     pressure  has  twice  the  diameter 

\ 

\ 

co- 

N 

\ 

\ 

\ 

\ 

50  V-N. 

m 

-^ 

\ 

A 

\ 

s 

40- 

\ 

V. 

*N 

i 

\ 

^> 

"  --  ^ 

i 

30- 

I 

•""    b 

E 

x^~  *•  •*  . 

^ 

M 

\ 

v       *• 

0 

—  B 

^"--2. 

~H 

-" 

20 

V     b 

c 

d 

e 

f 

"  

- 

t 

ATMO! 

iPHEP.E 

0                12345078 

n 

•Tfr.Xl 

FlG.  21. 

of  the  high  with  the  same  length  of  stroke.     The  scales  are  60  for 
the  high  and  20  for  the  low. 

In  order  to  be  at  all  comparable  the  diagrams  must  be  reduced 


RE-SCALING  THE   HIGH   PRESSURE  DIAGRAM. 


to  the  same  scale,  and  we  must  either  re-draw  the  high  pressure 
to  a   20  scale  or  the  low   to  a  scale  of  60.     It  will  be  more 

satisfactory  to  enlarge  than  to 
reduce,  for  a  slight  inaccuracy  of 
measurement  is  of  less  import- 
ance when  working  upon  a  coarse 
than  upon  a  fine  scale.  On  a  20 
scale  each  point  of  the  high 
pressure  diagram  will  be  60-^20= 
3  times  as  far  from  the  atmos- 
pheric line  as  on  a  60  scale,  for  it 
takes  three  inches  now  to  repre- 
sent the  pVessure  that  one  inch 
represented  before.  This  process 
is  shown  in  Fig.  21,  where  o  A  is 
3  times  oat  iB  3  times  -id,  iM  5 


FIG.  22. 


times  im,  etc..  and  the  dotted  outline  gives  the  diagram  as  it 
would  have  appeared  if  taken  with  a  20  spring. 


COMPARING  COMPOUND   DIAGRAMS  OE  THE  SAME   PRESSURE  SCALE.      31 

Having  now  our  diagrams  upon  -the  same  scale  we  can  com- 
pare them,  in  a  way,  by  reversing  one  of  them  and  placing  them 
together  so  that  the  atmospheric  lines  coincide,  as  in  Fig:  '22.  This, 
•while  it  shows  us  -nothing  of  the  continuous  action  of  the  steam  as 
compared  with  the  theoretically  plotted  diagram,  does  show  the 
loss  between  the  cylinders,  the  rise  of  pressure  in  the  high  pressure 
cylinder  after  the  cut-off  takes  place  in  the  low,  etc.,  and  is  par- 
ticularly instructive  in  engines  of  the  Wolff  or  receiverless  type, 
where  the're  is  no  cut-off  on  the  low  pressure  cylinder  and  the 


FIG.  23. 

steam  passes  directly  from  one  cylinder  to  the  other.  Such  a 
diagram  is  shown  in  Fig.  23,  from  a  pumping  engine  where  the 
steam  line  of  the  low  pressure  diagram  follows  the  back  pressure 
line  of  the  high  pressure  diagram  remarkably  close,  the  difference 
representing  the  frictional  resistance  to  the  flow  of  steam  through 
the  ports. 

We  have  seen  that  the  length  of  the  diagram  represents  vol- 
umes. The  lengths  of  the  cylinders  being  the  same,  their  volumes, 
will  be  proportional  to  the  squares  of  their  diameters,  and  as 
the  diameter  of  the  large  cylinder  is  twice  that  of~"lhe  .small,  its 
volume  will  be  four  times  the  volume  of  the  small.  Now  if  ,thfc 


REDUCING  THE  DIAGRAM   TO   THE  COMMON   VOLUME  SCALE. 


total  length  of  the  diagram  represents  the  volume  of  the  low  pres- 
sure cylinder  it  is  clear  that  the  diagram  of  the  high  pressure 
cylinder,  representing  only  one-quarter  of  that  volume,  should  be 
only  one-quarter  as  long.  When  the  piston  of  the  high  pressure 

cylinder  reaches  the  end  of  its 
stroke  the  steam,  cut  off  at  about 
a  quarter,  occupied  four  of  its 
original  volumes  at  a  pressure  of 
about  30  pounds. .  At  the  end  of 
the  low  pressure  stroke  it  occu- 
pied about  1 6  volumes  at  a  pres- 
sure of  about  "jYz  pounds.  We 
must  then  reduce  the  diagram  to 
the  same  scale  of  volumes  as  well 
as  of  pressures,  by  making  the 
length  of  the  high  pressure  dia- 
gram bear  the  same  proportion  to 
the  length  of  the  low  that  the 


FIG.  24. 

volume  of  the  high  pressure  cylinder  bears  to  the  volume  of  the  low  ; 
in  this  case  by  reducing  it  to  one-quarter  of  the  length  of  the  low 
pressure  diagram.  This  is  done  in  Fig.  24,  where  the  diagram  is 
divided  into  eight  equal  parts  by  the-ordinates  A  B  CD  EFG  HL 
One-quarter  of  its  length  is  then  divided  into  the  same  number 


THE  COMBINED   DIAGRAM. 


110- 


of  equal  parts  by  the  ordinates  a  b  c  d  e  f  g 
h  i.  The  pressures  are  then  transferred 
from  the  ordinates  in  the  full  length  dia- 
gram to  the  corresponding  ordinates  in  the 
shortened  diagram.  The  pressures  on  Y 
and  Z  for  instance,  on  ordinate  B  are  trans- 
ferred to  y  and  2-  on  ordinate  b.  When  this 
has  .been  done  for  all  the  ordinates  and  a 
line  drawn  through  the  points  so  located 
we  get  the  contracted  diagram  shown  on  the 
left.  Now  place  this  over  the  low  pres- 
sure diagram  with  the  atmospheric  lines 
coinciding  as  in  Fig.  25,  and  we  have  a 
combination  which  represents  the  continu- 
ous action  of  the  steam  through  the  sixteen 
expansions,  and  we  can  construct  the  theo- 
retical diagram  around  it  and  compare  the 
actual  with ;  the  theoretical  efficiency.  The 
area  between  them  indicates  the  losses  by 
failure  to  realize  initial  pressure  in  the  high 
pressure  cylinder,  wire  drawing,  losses  be- 
tween the  cylinders,  compression  and  by  an 
imperfect,  realization  of  the  vacuum  in  the 
Jow  pressure  cylinder. 

TO  RECAPITULATE. 

The  process  of  combining  the  diagrams 
from  a  compound  engine  consists  : 


FIG.  25. 


First,  in  reducing  the  diagrams  to  the  same  scale.  Divide 
the  scale  of  the  high  pressure  diagram  by  the  scale  of  the  low  and 
multiply  the  distance  of  every  point  in  the  high  pressure  diagram 
from. the  atmospheric  line  by  the  quotient. 


54  SUMMARY. 

Second,  in  reducing  the  diagrams  to  the  same  scale  of  volume'". 
Divide  the  volume  of  the  low  pressure  cylinder  by  the  volume  of 
the  high  and  divide  the  length  of  the  high  pressure  diagram  or 
multiply  the  length  of  the  low  by  the  ratio  of  the  cylinders  thus 
obtained.  When  the  stroke  is  the  same  in  both  cylinders  the  ratio 
may  be  obtained  by  dividing  the  diameter  of  the  high  and  squaring 
the  quotient. 

You  will  notice  that  I  have  not  complicated  this  demonstration 
of  the  combination  of  diagrams  by  the  introduction  of  clearance. 
When  clearance  is  involved  locate  the  clearance  line  on  each  dia- 
gram in  the  usual  way,  either  by  increasing  the  length  of  the  dia- 
gram in  accordance  with  its  known  percentage  of  clearance  or 
graphically  as  explained  above,  and  in  combining  make  the  clear- 
ance lines  as  well  as  the  atmospheric  lines  coincide. 


RECEIVERS. 


I  have  received  several  letters  lately  which  indicate  that  the 
above  subject  is  under  discussion,  and  in  looking  it  up  for  the  pur- 
pose of  replying,  I  find  that  there  is  more  to  it  than  there  seems  to 
be  and  that  it  is  not  well  understood.  Even  the  books  are  mis- 
leading. Seaton,  in  his  Manual  of  Marine  Engineering,  says, 
page  131 

' '  The  space  between  the  valve  of  the  high  pressure  cylinder 
and  that  of  the  low  pressure  cylinder  into  which  the  steam  exhausts 
from  the  high  pressure  cylinder  should  be  from  i  to  1.5  times  the 
capacity  of  the  high  pressure  cylinder  when  the  cranks  are  set  at  an 
angle  of  from  120  to  90  degrees.  When  the  cranks  are  opposite, 
or  nearly  so,  this  space  may  be  very  much  reduced.  The  pressure 
in  the  receiver  should  never  exceed  half  the  boiler  pressure  and  is 
generally  much  lower  than  this.  *  *  *  *  The  receiver 
of  three  crank  engines  need  not  be  nearly  so  large,  as  the  cranks 
are  usually  at  angles  of  1 20  degrees  ;  in  the  case  of  triple  compound 
engines  with  the  middle  pressure  leading  the  high  pressure  a  very 
small  fec.eiver  will  do." 

This,  if  I  read  it  correctly,  means  that  'a  cross  compound  with 
cranks  at  90  degrees  would  require  a  larger  receiver  than  a  tandem 
where  we  have  the  same  relation  between  the  exhausts  from  the 
high  pressure  cylinder  to  the  receiver  and  the  drafts  by  the  low 
pressure  cylinder  from  the  receiver  that  we  have  in  an  engine  with 
cranks  at  1 80  degrees.  Also  that  an  engine  with  cranks  at  120 
degrees  would  require  a  much  smaller  receiver  than  either.  Let 
us  see  whether  these  conclusions  are  borne  out  by  analysis. 

We  will  assume  an  engine  with  the  low  pressure  twice  the 
diameter  of  the  high.  With  the  same  stroke  its  volume  would  be 
four  times  that  of  the  high.  Let  there  be  no  clearance  in  either 
cylinder  and  let  the  receiver  equal  half  the  capacity  of  the  high 
pressure  cylinder.  The  initial  pressure  is  1 20  pounds  absolute,  and 


TANDEM-COMPOUND   RECEIVERS. 


cut-off  takes  place  at  quarter  stroke  in  both  cylinders.  Let  the 
expansion  be  isothermal  or  hyperbolic ,  that  is,  doubling  the 
volume  will  halve  the  pressure,  increasing  the  volume  to  three  times 
its  original  size  will  divide  the  pressure  by  3,  etc.  Under  these 
conditions  the  product^of  the  volume  and  pressure  will  be  constant 


FIG.  26. 


and  the  pressure  at  any  volume  can  be  found  by  multiplying  the 
original  pressure  and  volume  together  and  dividing  by  the  new 
volume,  always  remembering  to  use  the  absolute  pressure.  For 
example,  in  the  diagram,  Fig.  26.  we  have  at  the  point  of 
cut-off  G  what  we  will  call  one  volume  of  steam  at  120  pounds 
absolute.  At  H  this  has  been  expanded  to  2  volumes  and  we 
should  have 


TANDEM-COMPOUND  RECEIVERS.  37 

At  /  the  original,  i  volume  has  been  expanded  to  3  volumes  and 
the  pressure  would  be 

L> 

At  the  completion  of  the  stroke  J  we  have  four  volumes  and  the 
pressure  would  be 


In  each  case,  you  see,  the  product  of  the  pressure  and  volume  is 
constant 

2  x  60=  120 

3x40  =  120 

4X30=120 

I  X  I2O=  I2O 

Let  us  first  consjder  the  case  of  the  tandem  compound,  and 
first  let  me  remind  you  that  the  low  pressure  cylinder  must  take 
out  of  the  receiver  at  each  stroke  as  much  steam  as  the  high  pres- 
sure cylinder  delivers  to  it.  It  obviously  cannot  continuously 
take  out  of  the  receiver  more  than  is  put  into  it,  and  if  it  did  not 
take  out  as  much  the  steam  would  accumulate  in  the  receiver  and 
the  pressure  increase  until  the  high  pressure  cylinder  could  not 
exhaust  into  it.  It  may  take  out  a  greater  volume  than  the  high 
pressure  cylinder  delivers,  but  at  lesser  pressure,  or  it  may  take 
out  a  lesser  volume  at  a  greater  pressure,  but  the  product  of  the 
volume  and  the  pressure  of  steam*  taken  out  by  the  low  pressure 
cylinder  must  equal  the  product  of  the  volume  and  the  pressure 
of  the  steam  delivered  by  the  high  pressure. 

When  the  high  pressure  piston  was  at  the  right  hand  end  of 
the  cylinder  in  the  position  E  F  on  the  diagram  Fig.  26,  steam  was 
admitted  through  the  valve  represented  by  the  black  square  at  F 
in  position  A,  Fig.  27,  and  attaining  a  pressure  of  120  pounds  ab- 
solute was  continued  until  the  piston  reached  the  position  G  D, 
where  it  was  cut  off,  giving  us  the  volume  represented  by  the 
rectangle  G  FED,  in  both  Figs.  26  and  27,  to  work  with.  When 
the  piston  reached  the  end  of  the  stroke  as  at  position  A,  Fig.  27, 
this  has  been  expanded  to  four  volumes  at  30  pounds,  as  explained 
before.  These  four  volumes  at  30  pounds  will  be  delivered  at  each 
stroke  to  the  receiver.  Pass  now  to-  position  B,  where  the  quar- 
ter stroke  in  the  other  direction  has  been  reached,  and  both  cylih- 


TANDEM-COMPOCND   RECEIVERS. 


ders  are  ready  to  cut  off.     The  total  volume'  of  the  low  pressure 

cylinder  is  four  times  that  of  the  high.     Then  one-quarter  of   its 

volume  is  just  equal  to  the  whole  volume  of  the  high.     The  high 

pressure  cylinder  delivers  to  the  receiver  four  volumes  at  30  pourids 

pressure,   the  low  pressure  cylinder  at  quarter  cut-off  takes  out 

four  volumes,  and  necessarily,  as 

I  have  just  explained,  at  the  same 

pressure.      The    high    pressure 

cylinder,  receiver  and  low   pres- 

sure cylinder  are  all    open    to 

each  other,  as  shown  in  position 

&,  so  the  pressure  throughout  at 

this   point   must   be   30   pounds. 

On  ordinate  B,   Fig.    26,   repre- 

senting the  position  of  the  piston, 

at  this  time  set  off  at  L  30  pounds 

as  th£  back  pressure  in  the  high 

pressure  cylinder  and  the  receiver 

at  this  point.     While  the  pistons 

are  still  in  position  B,  the  valve 

between  the  low  pressure  cylinder 

and  the  receiver  closes,  shutting 

into  the  receiver  and  high  pres- 

sure cylinder  2-^-3=5  volumes  of 

steam  at  30  pounds  pressure. 

There  is  now  no  outlet  from  the 

receiver  and    the  further  move- 

ment of  the  high  pressure  piston 

to  the  right  must   compress  this 

steam 

At  position  C  or  half-stroke, 
we  have  two  volumes  in  the  re-  FIG.  27. 

ceiver  and  two  in  the  high  pres- 

sure cylinder,  four  in  all.  What  is  the  ^pressure  ?  Multiply  the 
termer  volume  5  by  the  corresponding  pressure  30,  and  divide  by 
the  new  volume 


This  is  the  receiver  pressure  and  the  back  pressure  in  the  smaller 


TANDEM-COMPOUND  RECEIVERS. 


cylinder  at  the  middle  of  the  stroke.     We  will  set  it  off  at  Mon 
the  ordinate  C  H  representing  that  position. 

At  position  D  the  five  volumes  at  30  pounds  have  been  com- 
pressed to  2-f  1=3  volumes.     The  pressure  is 


We  will  set  this  off  at  N  on  ordinate  D,  representing  this  position 
on  the  diagram. 

At  position  E  the  five  volumes  at  30  pounds  have  been  com- 
pressed to  the  two  volumes  of  the  receiver,  the  pressure  is 


Set  this  off  on  P  on  the  ordinate,  E  representing  this  positiori~on 
the  diagram  Connecting  the  points  L  MNP  we  have  the  curve 
representing  the  increase  ot  pressure  in  the  receiver  and  high  pres- 
sure during  the  last  three-quarters  of  the  stroke. 

Now  we  have  a  receiver  containing  two  volumes  of  steam  at 
75  pounds  pressure.  At  the  end  of  the  stroke  this  will  be  opened 
to  a  high  pressure  cylinder  containing  four  volumes  at  30  pounds. 
The  conditions  will  be  practically  as  at  position  A  only  that  it  is 
the  other  ends  of  the  cylinders  that  are  involved  We  must  multi- 
ply each  volume  by  its  own  pressure  and  divide  the  sum  of  the 
products  by  the  sum  of  the  volumes.  This  will  give  us  the  pressure 
of  the  mixture 

75  X  2  =  150 
30  x  4=  120 


This  will  be  the  pressure  at  position  A  Setting  it  off  at  K  on 
ordinate  A,  Fig.  26,  we  see  that  when  the  exhaust  valve  opened 
between  the  high  pressure  cylinder  and  the  receiver  the  back 
pressure  increased  to  45  pounds  on  account  of  the  higher  pressure 
in  the  receiver  as  a  result  of  the  compression  during  the  last 
three-quarters  of  the  stroke.  As  the  pistons  move  to  position  B, 
the  steam  will  expand  to  30  pounds  on  the  line  K  L,  completing 
the  counter  pressure  line  of  the  high  pressure  cylinder,  which  Jine 
alsb  shows  the  variation  of  pressure  in  the  receiver.  K  L  is  the 
steam  line  of  the  low  pressure  cylinder,  and  the  expansion  would 


TANDEM-COMPOUND   RECEIVERS. 


continue  along  the  dotted  line,  making  the  diagram  K  L  Q  E  A  for 

the  low  pressure.     Since  the  low  pressure  piston  has  four  times  the 

area  of  the  high,  one  foot 
of  movement  will  generate 
four  times  as  much  volume 
in  the  larger  cylinder.  In  or- 
der to  be  comparable  then 
the  high  pressure  diagram 
must  be  reduced  one-fourth 
the  length  of  the  low.  Re- 
ducing its  length,  leaving 
the  vertical  scale  the  same, 
and  placing  it  over  the  low 
pressure  diagram  as  in  Fig. 
28,  we  have  the  combined 
diagram  showing  the  com- 
plete expansion  from  120  to 
7 J^  pounds.  The  two  black 
portions  are  lost  work  but 
the  cross  hatched  area  at  A 

where  the  diagrams  overlap,  represents  double  that  area  of  useful 

work. 

At  B   5  vols.  at  30  =150 
At  C   4  "   "  37-5  =  150 


FIG. 


At  D 
At  E 

At  A 


At  B> 


37-5  = 

50  = 

75  = 

75  = 

30  = 
45 
30 


150 
150 
150 
1 20 
"270 
270 


You  see  in  Fig.  26  tint  the  high  pressure  diagram  loops  at 
the  end  of  the  expansion  line.  To  avoid  this  loop  altogether  we 
should  have  to  cut  off  at  one-half  stroke  in  the  low  pressure  cylin- 
der, with  the  ratio  giving  us  the  back  pressure  line  J  R  S  T  Uior 
the  high  pressure  cylinder,  and  giving  that  cylinder  a  large  varia- 
.tion  of  temperature  and  by  far  the  most  of  the  load.  As  the  size 
of  the  receiver  is  increased,  the  line  of  back  pressure  becomes 
more  nearly  straight,'  V  f  showing  its  appearance  when  the  receiver 
is  equal  to  the  volume  of  the  high  pressure  cylinder,  W.  f^when 
it  equals  two  such  volumes  and  K  K  when  it  equals  five;  such 


CROSS-COMPOUND   RECEIVERS. 


volumes,  but  notice  that  only  when  the  receiver  becomes  infinitely- 
large  shall  we  get  rid  theoretically  of  the  end  loop,  because  the 
pressure  in  the  receiver  at  the  end  of  the  stroke  is  bound  under  our 
assumed  conditions  to  be  greater  than  that  in  the  high  pressure 
cylinder. 

Now  for'the  cross  compound  with  crank  at  90  degrees,  and 


POSITION  0.      4.03  VOLS.   44.1  L8S. 


POSITION  E.  6. 27  VOLS.  30  LBS. 

AFTER  CUT-OFF 
2.27  VOLS.  AT  30  POUNDS 


POSITION  F.     2  VOLS.    34.  OS 


FIG.  29. 

here  too  we  must  commence  at  the  point  of  cut-off  in  the  low  pres- 
sure cylinder,  as  this  is  the  only  point  at  which  we  are  sure  of  the 
receiver  pressure.  This  will  be  at  position  E,  Fig.  29,  when  the 
Jow  pressure  piston  is  at  quarter  stroke.  If  you  will  look  at  the 
relative  position  of  the  cranks  for  this  position  you  see  that  the 


|2  CROSS-COMPOUND   RECEIVERS. 

high  pressure  piston  will  have  nearly  completed  its  stroke,  leaving 
only  .27. 

The  high  pressure  crank  is  30  degrees  from  the  horizontal. 
The  versed  sine  of  30  (  =  i -the  cosine)  is  i_. 866025=.  133975. 
This  would  be  the  distance  of  the  piston  from  the  end  of  the  stroke 
if  the  crank  was  i,  but  the  length  of  the  crank  represents  2  of  our 
units  of  volume,  the  stroke  being  4,  so  the  volume  between  the 
piston  and  cylinder  head  in  position  E  is  .  133975x2=.  267950 
or  .  27  nearly,  of  one  of  our  original  volumes  in  that  cylinder.  The 


valve  between  the  receiver  and  the  low  pressure  cylinder  closing  at 
this  point  leaves  2+ .27=2/27  volumes  at  30  pounds. 

Now  on  diagram  Fig.  30  locate  ordinate  £,  representing  the 
position  of  the  high  pressure  piston  at  this  time.  The  length  of 
the  stroke  represents  4  volumes,  the  uncompleted  portion  of  one 
volume,  so  the  piston  will  be  .27 x. 25=. 0675  of  the  stroke  from 
the  end.  On  this  ordinate  when  located,  set  off  30  pounds,  repre- 
senting the  pressure  in  the  receiver  and  high  pressure  cylinder  at 
this  point 

When  the  high  pressure  piston  reaches  the  end  of  its  stroke 
the  2. 27  volumes  will  be  compressed  to  2  as"  shown  in  position  /• 
and  the  pressure  will  be 


CROSS-COMPOUND   RECEIVERS. 


34.05  Ibs. 


Set  off  this  pressure  on  ordinate  F.  When  the  high  pressure 
cylinder  releases  on  the  other  side  by  opening  the  valve  A  at  posi- 
tion F  we  add  to  this  four  volumes  at  30  pounds,  with  a  resulting 
pressure  of 

34.05  x  2  =      68.1 

30          X    4  —     120. 
6       (188.1 

31.35  «». 

Set  off  this  pressure  on  ordinate  A. 

At  B  this  six  volumes  at  31.35  pounds  will  be  reduced  to  five 
volumes  and  the  pressure  will  be 

6  x  3I-35  =  37.62  Ibs. 

which  we  set  off  on  ordinate  B. 

At  C  the  volume  is  reduced  to  four  and  the  pressure 

6  x  3i-3< 


4          x  47-025 

Set  this  off  on  ordinate  C. 

At  position  D  the  low  pressure  piston  has  moved  as  far  from 
the  cylinder  head  as  the  high  pressure  was  in  position  /•*,  giving  four- 
times  the  volume  the  high  pressure  gave  in  the  same  position. 

4  X.  27=  i.  08  volumes. 

There  is  still  one  volume  in  the  high  pressure  cylinder  and 
the  total  volume  including  the  receiver  is 

i.  08  +  i  +  2  =  4.08 
The  pressure  is 


fl 
4.08 

Set  this  off  on  D. 

.Between  Cand-Z?  we  have  had  at  first  compression  because 
the  low  pressure  piston  while  near  the:  center  moved  away  less 
than  one-quarter  as  fast  as  the  high.  When  for  an  instant  it 
moved  just  ofte-quarter  as  fast,  as  the  high  the  volume  was  con- 
stant and  the  pressure  neither  rose  nor  fell.  Then*  as  the  low 
pressure  piston  gained  in  speed  relatively  to  the  high,  the  volume 
increased  and  the  pressure  fell  to  46.  i  pounds  at  D.  I  have  fig- 
ured the  intermediate  volumes  and  pressures  and  plotted  the 


CROSS-COMPOUND   RECEIVERS 


curve  as  you  see  it  in  Fig.  30,  but  will  not  weary  you  with  the 
details. 

At  E  we  have  6. 27  volumes  and  the  pressure  is  as  it  should  be 


•6  x  31.35 
6.27 


=  30  Ibs. 


Connecting  the  various  points  which  we  have  set  off  on  the  ordi- 
nates  with  the  curve  shown  we  get  the  contour  of  the  back  press- 
ure line  and  complete  the  high  pressure  diagram.  Notice  that  the 
exhaust  goes  direct  to  the  low  pressure  cylinder,  that  is  the  receiver 
is  open  to  both  cylinders  from  position  C  to  position  E,  nearly 


FIG 


FIG.  32. 


half  the  stroke.  The  steam  line  of  the  low  pressure  diagram  is 
that  portion  of  the  counter  pressure  line  of  the  high  pressure 
diagram  which  lies  between  ordinates  C  and  E,  and  this,  somewhat 
changed  in  shape  by  being  referred  to  the  ordinates  which  repre- 
sent the  corresponding  volumes  in  the  first  quarter  of  the  low 
pressure  stroke,  is  shown  by  the  dotted  steam  line  of  the  low 
pressure  cylinder  between  A  and  2?»  the  expansion  continuing 
regularly  from  B  as  before,  giving  us  the  complete  low  pressure 
diagram.  These  are  combined  in  Fig.  31.  The  blackened  area 
is  minus,  ihe  shaded  area  where  the  diagrams  overlap  has 
double  value.  They  appear  to  be  so  nearly  equal  that  there 
can  be  little  loss. 


CROSS-COMPOUND  RECEIVERS. 


45 


At  E 

2;  27    VC 

Is.  a 

t  30         = 

68.1 

At  F 

.2 

1 

34.05    = 

68.1 

At  A- 

[2 

.< 

34-05    = 

68.1 

14 

1 

3°         =. 

1  20 

6 

31-25    =" 

788. 

At  B 

5 

37-62    = 

188. 

At  C 

4 

47.025  = 

1  88. 

At  D 

4.08 

46.1      = 

188. 

At  E 

6.27 

30         = 

1  88. 

cross  compounds  at  90  degrees. 

Let  us  look  now  at  the  cross  compound  with  cranks  at 
the  low  pressure  leading.  Cut-off  in  the  low  pressure  cylinder 
will  take  place  when  the  pistons  are  in  positio'n  E  Fig.  33,  and 
when  the  valve  closes  we  shall  have  three  volumes  at  30  pounds,. 
which  at  position  F  is  compressed  to  2  volumes  at 


42  Ibs. 


Now  the  valve  at  A  opens  allowing  4  volumes  at  30  pounds  to- 
mingle  with  2  volumes  at  45  pounds,  and  we  get  a  resulting  pres- 
sure of 

45  X  2  =    90 

30  x  4  =  120 

6    )  2  ip 

~35lbs. 

At  position  B  the  low  pressure  cylinder  has  not  yet  taken  any 
steam  from  the  receiver  and  we  have  5  volumes  with  a  pressure  of 

6  X  35 

A  Cthe  low  pressure-  crank  is  30  degrees  below  the  horizontal  and 
the  same  volume  will  have  been  generated  as  in  the  similar  position 
D,  Fig.  29,  This  we  found  to  be  1.08.  The  Total  volume  at  this. 
point  then  is  5.08  and  the  pressure 

6x  35 
5-08 

At  position  D  the  high  pressure  piston  has  advanced  another 
eighth,  and  the  low  has  opened  2.294  volumes.  I  will  .ask  you  to 
take  my  word  for  this  and  not  bother  you  with  the  details  of  its- 
calculation.  The  total  volume  will  be  5.794  and  the  pressure 

6  x  35 

5-794 


'-  41.34 


=  36. 26  Ibs. 


46 


CROSS-COMPOUND   RECEIVERS. 


At  E  we  have  one  volume  in  the  high  and  two  in  the  receiver, 
which,  with  the  4  in  the  low,  make  7  in  all  and  the  pressure  will 
be 


Setting  off  these  pressures  on  their  respective  ordinates  and 


2  VOLS.AT  45  LBS. 


2  VOLUMES 


POSITION  A.   6  VOLS.  35  LBS.  POSITION  B.   S  VOLS.  42  LBS.  POSITION  C.  *.  08  VOLS.  41.  34  LBS. 


Ftc.  33. 

drawing  the  curves  through  them  we  get  the  back  pressure  line 
shown  in  Fig.  32.  •  The  receiver  is  open  to  both  cylinders  during 
a  full  half  of  the  high  pressure  stroke,  from  position  B  to  position 


CROSS-COMPOUND   RECEIVERS. 


47 


E,  and  that  part  of  the  back  pressure  line  is  contracted  to  form 
the  dotted  steam  line  of  the  low' pressure  cylinder.  The  combined 
diagrams  are  shown  in  Fig.  34,  where  as  before,  the  back  spaces 
represent  minus  area  and  the  cross-hatched  spaces  area  of  double 
value.  The  high  pressure  diagram  loops  more  and  there  is  an 


FIG.  34. 


FIG.  35. 


excess  of  black  space,  but  the  variation,  from  30  to  43  pounds,  is 
not  so  great  as  in  either  of  the  other  cases. 


At  E        3  vols.  at  30 


At  F 
At  A 


At  B 


\\ 


At  C  5-og 
At  D  5.794 
At  E        7 


45 

45 

30 

35 

42 

41-34 

36.26 

30 


=    90 

=    90 

=  90 
=  1 20 

=  2IO 
=  2IO 
=  2IO 
=  2IO 
=  2IO 


With  cranks  opposite  neither  can  be  said  to  lead  for  one  is 
as  much  ahead  of  the  other  as  the  other  is  ahead  of  it.  With 
cranks  at  90°  it  apparently  makes  no  difference  which  leads,  for  as 


48 


CROSS-COMPOUND   RECEIVERS. 


shown  by  the  dotted  cranks  in  Fig.  29  the  low  pressure  crank 
would  be  in  the  same  position  with  reference  to  the  other  end  of 
the  cylinder  that  it  bears  to  the  end  as  shown.  With  cranks  at 
120°,  however,  it  does  make  a  difference,  for  instead  of  leading 
the  high  pressure  crank  as  in  Fig.  33  the  low  pressure  crank  fol- 


POSITION  8.   5  VOLS.  AT  36 


POSITION  C.  4  VOLS.  AT  45 


POSITION  0.  3  VOLS.  AT  60 


POSITION  F.   C  VOLS.  AT  30 


FIG.  36. 

lows  the  high  as  in  Fig.  36,  the  high  pressure  piston  will  be 
commencing  its  stroke  when  cut-off  occurs  in  the  low  as  at  posi- 
tion A  Fig.  36,  instead  of  having  one-quarter  to  go  as  at  E  Fig.  33. 
Calculating  the  pressures  for  the  various  positions  of  the  pistons 
as  in  the  other  cases,  we  get  the  receiver  pressure  line  shown  in 


CROSS-COMPOUND   RECEIVERS 


49 


Fig.  35  and  the  combined  diagram  shown  in  Fig.   37,  where,  as 
before,  the  black  area  is  minus  and  the  shaded  area  of  double  value. 
Time  does  not  permit  of  a  discussion  of  the  comparative  desi- 
rability of  these  different  methods  of  distribution  nor  a  considera- 


FIG.  37. 

tion  of  the  effect  oi  an  increase  of  cylinder  ratios  to  avoid  the  loop. 
I  should  say,  however,  that  the  diagram  shown  by  the  tandem  was 
the  worst  of  all,  and  it  is  not  apparent  how  it  can  get  along  with  a 
smaller  receiver  than  the  others. 


INDEX. 


Actual  and  ideal  diagram,  27 

diagram.    Drawing  the  ideal  and,  28 


Dividing  the  diagram  for  equal  work,  16 
Drawing  the  ideal  and  actual  diagram, 

28 
•Drop,  Effect  of,  22 


Combined  diagram,  15 
Combining  diagrams,  26-34 

Rules  for,  33 
Comparing  compound  diagrams  with  the 

ld*eal,  29 
diagrams,  31 

Complete  expansion  diagram,  40 
Compound    diagrams.     Comparing    with 

the  ideal.  29 
receivers.    Cross,  41-49 

tandem,  36-40- 
Condensation  cylinder,  5 
effect  of  cylinder,  6 
surface  involved  in  initial,  7 
Conventional  diagram,  The,  14 
Cross  compound  receivers,  41-49 
Cut-off  in  low  pressure  cylinder,  11 
Cylinder  condensation,  5 

effect  of,  6 
Cut-off  in  low  pressure,  11 

volume  of  steam  taken  by  low  pres- 
sure, 37 
Cylinders.     Mean    pressure    referred    to 

low  pressure,  13 

use  of  two  to  complete  expansion,  9 
three  or  more,  23 


Diagram.    Actual  and  Ideal,  27 
combined,  15 

dividing  for  equal  work,  16 
drawing  the  ideal  and  actual,  28 
of  complete  expansion,  40 
reducing  the  high  pressure,  14 

to  the  common  volume  scale,  32 
re-scaling  the  high  pressure,  30 
the  conventional,  14 

Diagrams.    Combining,  26-34 
comparing,  31 

compound  with  the  Idea!,  29 
rules  for  combining,  33 


Effect  of  cylinder  condensation,  6 

drop,  22 

receiver,  25 

variable  load,  17 
Efficiency  due  to  high  pressure,  8 
Equal  work.    Dividing  the  diagram  for, 

16 
Expansion  diagram.   Complete,  40 

gain  by,  3 

limit  of  gain  by,  4 

rules  for  finding  ratio  of,  1 

total  ratio  of,  10 

use  of  two  cylinders  to  complete,  9 

total  advisable,  20 

Expansions.    How  to  compute  the  total, 
12 


Figuring  receiver  pressure,  38 


Gain  by  expansion,  3 
limit  of,  4 

H 

High   pressure  diagram.    Reducing   th«. 

14 

re-scaling  the,  30 
efficiency  due  to,  8 
Horse  power.    Required  least  amount  of 

steam  per,  18 
How  to  compute  the  total  expansions,  12 


Ideal  and  actual  diagram,  27 

drawing.   28 

Initial    condensation.     Surface   involved 
In.  7 

pressure.    Rule  for  finding,  2 


Limit  of  gain  by  expansion,  4 

Load.    Effect  of  variable,  17 

Loop.    To  avoid  the,  40 

Low  pressure  cylinder.    Cut-off  in,   11 
volume  of  steam  taken  by,  37 
cylinders.     Mean    pressure    referred 
to,  13 


Mean   pressure  referred  to  low  pressure 
cylinder,  13 


Rules  for  combining  diagrams,'  33 

finding  initial  pressure,  2 

ratio  of  expansion,   1 

terminal  pressure,  2 


Size  of  receiver,  24 

Steam   per  horse-power     Required   least 

amount  of,   18 

volume  taken   by   low  pressure  cyl- 
inder, 37 

Surface    involved    in    initial    condensa- 
tion, 7 


Points  to  remember,  19 

Pressure   diagram.    Reducing   the    high, 

14 

efficiency  due  to  high,  8 
figuring   receiver,   38 
referred  to   low  pressure  cylinders 

Mean,  13 
rule  for  finding  initial,  2 

terminal,  2 
terminal,  18 


Tandem:    Compound  receivers,  36-40 
Terminal  pressure,  18 

rule  for  fin'ding,  2 
The  conventional   diagram,   14 
To  avoid  the  loop,  40 
Total  expansions  advisable,  20 
how  to  compute,  12" 

latio  of  expansion,  10 
Two  cylinders.    Use  of  to  complete  ex 
pansion,  9' 


Ratio  of  expansion.    Total,  10 

rule  for  finding,  1 
Receiver.    Effect  of,  25 

pressure.     Figuring,   38 
size  of,  24 
Receivers,  35-49 

cross  compound,  41-49 

tandem  compound,  36-40 
Reducing-  the   diagram   to 'the   common 

volume  scale,  32 
high  pressure  diagram,  14 
Required    least    amount    of    steam    per 

horse-power,  18 
Re-scaling  the  high  pressure  diagram,  30 


Use  of  three  or  more  cylinders,  23 

two    cylinders    to    complete"  expan- 
sion, 9 


Variable  lead.    Effect  of,  17 
Volume  of  steam  taken  by  low  pressure 
cylinder.  37 

W 

Work.    Dividing  the  diagram  for  equal 
16 


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